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 Miscellaneous_Word_Problems/127989: 2) Pipe A can fill a tank in 4hr. Pipe B can fill the tank in 9hr less than the time it takes pipe C, a drain pipe, to empty the tank. When all three pipes are open, it takes 2hr to fill the tank. How much time is required for pipe C to empty the tank if pipes A and B are closed?1 solutions Answer 93738 by ankor@dixie-net.com(15636)   on 2008-02-20 15:51:39 (Show Source): You can put this solution on YOUR website! Pipe A can fill a tank in 4 hr. Pipe B can fill the tank in 9 hr less than the time it takes pipe C, a drain pipe, to empty the tank. When all three pipes are open, it takes 2 hr to fill the tank. How much time is required for pipe C to empty the tank if pipes A and B are closed? : Pipe C's draining time = x (when Pipes A & B are closed) : Pipes A's filling time = 4 hr (given) : Pipe B's filling time = (x-9) (Given as 9 hrs less than C) : Let the full tank = 1 : Filling is +, draining is - : The equation when all three are open for 2 hrs: + - = 1 : Multiply the equation by 4x(x-9) to get rid of the denominators: 4x(x-9)* + 4x(x-9)* - 4x(x-9)* = 4x(x-9)(1) Cancel out the denominators and you have: x(x-9)*2 + 4x(2) - 4(x-9)*2 = 4x(x-9) : 2x^2 - 18x + 8x - 8x + 72 = 4x^2 - 36x : 2x^2 - 4x^2 - 18x + 36x + 72 = 0 : -2x^2 - 18x + 72 = 0 : x^2 - 9x - 36 = 0; Divide by -2; simplifies and changes the signs Factors to (x + 3) (x - 12) = 0 Positive solution x = 12 hrs for the the drain to empty the tank with A & B closed : ; Check solution (B's fill time will be 12-9 = 3 hrs) + - = + - = = 1
 Exponents-negative-and-fractional/127889: A company distributes its product by train and by truck. The cost of distributing by train can be modeled as -0.07x^2+34x-135, and the cost of distributing by trucks can be modeled as -0.02x^2+24x-180, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by trucks. 1 solutions Answer 93711 by ankor@dixie-net.com(15636)   on 2008-02-20 12:53:30 (Show Source): You can put this solution on YOUR website!A company distributes its product by train and by truck. The cost of distributing by train can be modeled as -0.07x^2+34x-135, and the cost of distributing by trucks can be modeled as -0.02x^2+24x-180, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by trucks : Let f(x) = difference in cost between trains & trucks : f(x) = (-0.07x^2+34x-135) - (-0.02x^2+24x-180) : Removing the brackets changes the signs f(x) = -0.07x^2 + 34x - 135 + 0.02x^2 - 24x + 180 : f(x) = -.07x^2 + .02x^2 + 35x - 24x - 135 + 180 : f(x) = -.05x^2 + 11x + 45
 Linear-equations/127717: at a college prodution of streetcar named desire 400tickets were sold. the ticket prices were \$8, \$10, and \$12 and the total income from the ticket sales was 3700. how many tickets of each type were sold if the combined number of \$8 and \$10 tickets sold was 7 times the number of \$12 tickets sold?1 solutions Answer 93620 by ankor@dixie-net.com(15636)   on 2008-02-19 16:42:22 (Show Source): You can put this solution on YOUR website!prices were \$8, \$10, and \$12 and the total income from the ticket sales was \$3700. how many tickets of each type were sold if the combined number of \$8 and \$10 tickets sold was 7 times the number of \$12 tickets sold? : It says 400 tickets sold: x + y + z = 400 : It says: "prices were \$8, \$10, and \$12 and the total income from the ticket sales was 3700. 8x + 10y + 12z = 3700 : It says: "the combined number of \$8 and \$10 tickets sold was 7 times the number of \$12 tickets sold?" x + y = 7z x = (7z-y) : Using the 1st equation, substitute (7z-y) for x (7z-y) + y + z = 400 7z + z - y + y = 400 8z = 400 z = z = 50 ea \$12 ticket sold ; Substitute 50 for z in the 1st equation: x + y + 50 = 400 x + y = 400 - 50 x + y = 350 x = (350-y) : Subsitute 50 for z in the 2nd equation: 8x + 10y + 12(50) = 3700 8x + 10y + 600 = 3700 8x + 10y = 3700 - 600 8x + 10y = 3100 : Substitute (350-y) for x in the above equation 8(350-y) + 10y = 3100 2800 - 8y + 10y = 3100 2y = 3100 - 2800 2y = 300 y = y = 150 ea \$10 tickets : I'll let you find the number of \$8 tickets (x), there are several ways to do it.
 Numbers_Word_Problems/127730: The sum of two numbers is 6 less than twice the first number. Their difference is 10 less than four times the second number. Find each of the numbers1 solutions Answer 93614 by ankor@dixie-net.com(15636)   on 2008-02-19 14:56:29 (Show Source): You can put this solution on YOUR website!Let x = one number Let y = a second number : Write an equation for each statement; (where you see the word "is", you can usually put an = sign): : "The sum of two numbers is 6 less than twice the first number. x + y = 2x - 6 Simplify: y = 2x - x - 6 y = x - 6 : "Their difference is 10 less than four times the second number. x - y = 4y - 10 Simplify x = 4y + y - 10 x = 5y - 10 : Find each of the numbers : Substitute (x-6) for y (from the 1st equation); find x: x = 5(x-6) - 10 x = 5x - 30 - 10 x = 5x - 40 +40 = 5x - x 40 = 4x x = +10 : Find y using the 1st equation y = 10 - 6 y = 4 : : Check solutions using the statement: "Their difference is 10 less than four times the second number." 10 - 4 = 4(4) - 10 6 = 16 - 10; confirms our answer : How about this? Did it seem logical, and do you think you can handle these kind of problems now?
 Mixture_Word_Problems/127798: I have a 10-ounce glass of kool-aid that is 30% sugar. I want to make it less sweet. How much water can I add to the 30% solution to make it only 25% sugar.1 solutions Answer 93608 by ankor@dixie-net.com(15636)   on 2008-02-19 13:13:08 (Show Source): You can put this solution on YOUR website!I have a 10-ounce glass of kool-aid that is 30% sugar. I want to make it less sweet. How much water can I add to the 30% solution to make it only 25% sugar. : Let x = amt of water required to make it to reduce the sugar to 25% : A simple equation: .30(10) = .25(x+10) : 3 = .25x + 2.5 : 3 - 2.5 = .25x : .5 = .25x x = x = 2 oz of water required : : Check solution: .3(10) = .25(2+10) 3 = .25(12); confirms our solution
 Mixture_Word_Problems/127714: A painter works on a job for 10 days and is then joined by her helper. Together they finish the job in 6 more days. Her helper could have done the job alone in 30 days. How long would it have taken the painter to do the job alone?1 solutions Answer 93557 by ankor@dixie-net.com(15636)   on 2008-02-18 22:10:45 (Show Source): You can put this solution on YOUR website!A painter works on a job for 10 days and is then joined by her helper. Together they finish the job in 6 more days. Her helper could have done the job alone in 30 days. How long would it have taken the painter to do the job alone? : Let x = time required by the painter to do the job alone : Let the completed job = 1 : Think of of it this way. The painter has 10/x of the job completed when he's joined by the helper + + = 1 same as: + = 1 : Multiply equation by 30x to get rid of the denominator 30x* + 30x* = 30x(1) : 30(16) + 6x = 30x 480 + 6x = 30x 480 = 30x - 6x 480x = 24x x = x = 20 days, painter by himself : : We can check that using the original equation + + = + + = 1
 Exponential-and-logarithmic-functions/127650: I was absent and my friend got my homework for me. My homework is not from the textbook and I missed the instruction. Would someone please work this problem in easy to follow steps so I can figure out how to complete the rest of my assignment? PLEASE ? 7^(2x+3)=5^(x-4)1 solutions Answer 93556 by ankor@dixie-net.com(15636)   on 2008-02-18 21:49:04 (Show Source): You can put this solution on YOUR website! 7^(2x+3) = 5^(x-4) : Use natural logs to solve this: : Using the log equivalent of exponents, we can write it: : Find nat log (ln) of 7 and 5: 1.9459(2x+3) = 1.6094(x-4) : Multiply what's inside the brackets 3.8918x + 5.8377 = 1.6094x - 6.4376 : Some basic algebra 3.8918x - 1.6094x = -6.4376 - 5.8377 : 2.2824x = -12.2753 x = x = -5.378 : ; Check solution on a good calc: enter 7^(2(-5.378)+3) = 2.7888 enter 5^(-5.378-4) = 2.7865, close enough to check our solution ; : Did this make sense? You can use common logs (base 10) if you prefer, the method is the same. (the numbers will be different, but the answer will be the same)
 Numbers_Word_Problems/127562: This question is from textbook 1 If a number is added to the numerator of 3/4 and twice as much is added to the denominator, the result is 4/7. Find the number. 2. The sum of a number an its reciprocal is 13/6. Find the numbers. 3. An inlet pipe can fill an empty swimming pool in 5 hours, and another inlet pipe can fill the pool in 4 hours . How long will it take both pipes to fill the pool?1 solutions Answer 93517 by ankor@dixie-net.com(15636)   on 2008-02-18 15:28:21 (Show Source): You can put this solution on YOUR website!If a number is added to the numerator of 3/4 and twice as much is added to the denominator, the result is 4/7. Find the number. : Let the number to be added = x : = Cross multiply, and solve for x 4(2x+7) = 7(x+3) 8x + 28 = 7x + 21 8x - 7x = 21 - 28 x = -7 : Check solution in original equation, substitute -7 for x = = = ; minus into a minus is a plus : : 2. The sum of a number an its reciprocal is 13/6. Find the numbers. x + = Multiply equation by 6x to get rid of the denominators 6x(x) + 6x* = 6x* 6x^2 + 6 = 13x : 6x^2 - 13x + 6 = 0; a quadratic equation : After a little slogging, we find we can factor this to: (2x - 3)(3x - 2) = 0 : 2x = 3 x = and 3x = 2 x = : Check solution using x = 3/2: + = + = ; confirms our solution Note that the 2nd solution is the reciprocal of the 1st : : 3. An inlet pipe can fill an empty swimming pool in 5 hours, and another inlet pipe can fill the pool in 4 hours . How long will it take both pipes to fill the pool? : A typical shared work problem: Let t = time required when both pipes are open Let the full pool = 1 : + = 1 Multiply equation by a common multiple, 20 will work 20* + 20* = 20(1) Cancel out the denominators and you have: 4t + 5t = 20 : 9t = 20 t = t = 2.22 hrs or 2 hrs & 13.3 min : Check solution using 2.22 for t: + = 1 .444 + .555 = .999 ~ 1; confirms our solution : : Could you follow the procedures in all these problems? Let me know if you have any questions
 Probability-and-statistics/127434: The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood: each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of \$9 each, and tables will result in a profit of \$20 each. How many benches and tables should Outdoors Furniture produce to obtain the largest possible profit? Use graphical Linear programming approach.1 solutions Answer 93448 by ankor@dixie-net.com(15636)   on 2008-02-17 21:34:32 (Show Source): You can put this solution on YOUR website!The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood: each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of \$9 each, and tables will result in a profit of \$20 each. How many benches and tables should Outdoors Furniture produce to obtain the largest possible profit? Use graphical Linear programming approach. : Let x = no. of picnic tables Let y = no. of benches : The labor constraint: 6x + 4y <= 1200 4y <= 1200 - 6x; divide equation by 4 y <= 300 - 1.5x : Plot above equation for x = 0 and x = 60 x | y ------- 0 | 300 60 | 210 ; : The material constraint 35x + 10y <= 3500 10y <= 3500 - 35x y <= 350 - 3.5x; divide equation by 10 : Plot the above equation for x = 0 and x = 60 x | y ------- 0 | 350 60 | 140 : Graph will look like this The area of feasibility is at or below the two graphs, which ever is lowest Area is bounded by coordinates; 0,0; 0,300; 100,0; and an integer values of 25, 262 Find the profit using each: Tables + Benches 20(0) + 9(300) = \$2700 20(100) + 9(0) = \$2000 20(25) + 9(262) = \$2858; : 25 tables and 262 benches will yield max profit; utilizes: 6(25) + 4(262) = 1190 hrs of labor 35(25) + 10(262) = 3495 ft of red-wood : This is the general idea. Check my math here, a lot of chance for mistakes
 Quadratic_Equations/127467: Mary wants her \$9000 GIC to double in value in nine years. What annual rate of interest is required for her to reach her goal. Assume interest is compounded annually.1 solutions Answer 93429 by ankor@dixie-net.com(15636)   on 2008-02-17 20:17:15 (Show Source): You can put this solution on YOUR website!Mary wants her \$9000 GIC to double in value in nine years. What annual rate of interest is required for her to reach her goal. Assume interest is compounded annually. : Let r = decimal value of the interest required : Using the annual interest equation: A = Ao*(1+r)^t : 9000 * (1 + r)^9 = 18000 : (1 + r)^9 = 18000/9000; divided both sides by 9000 : (1 + r)^9 = 2 : 9 * ln(1+r) = .693 ln(1 + r) = ln(1 + r) = .077 : Find the antilog (e^x) of both sides 1 + r = 1.08 ; r = 1.08 - 1 : r = .08 which is 8% ; : Check solution using a calc 1.08^9 * 9000 = 17991 ~ 18000
 Quadratic_Equations/127471: Two die- cast metal car models were purchased at the same time. The first cost \$99.50 and appreciated by 10% yearly. The second cost \$49.50 and appreciated 16% yearly. Algebraically determine how many years will it take for the two models to be of equal value.1 solutions Answer 93417 by ankor@dixie-net.com(15636)   on 2008-02-17 20:00:28 (Show Source): You can put this solution on YOUR website!The first cost \$99.50 and appreciated by 10% yearly. The second cost \$49.50 and appreciated 16% yearly. Algebraically determine how many years will it take for the two models to be of equal value. : Use the annual interest equation, t = time in years : Cheap car value = expensive car value : 49.5(1.16)^t = 99.5(1.10)^t : Using natural logs: ln(49.5) + ln(1.16^t) = ln(99.50) + ln(1.10^t) : log equiv of exponents: ln(49.5) + t*ln(1.16) = ln(99.50) + t*ln(1.10) : 3.902 + .1484t = 4.6 + .0953t : .1484t - .0953t = 4.6 - 3.902 : .0531t = .698 t = t = 13.14 years ; : Find the value of each after 13.14 yrs, using a calc 1.16^13.14 * 49.5 = \$348 1.1^13.14 * 99.5 = \$348 confirms our solution
 Equations/127409: Can someone please help me solve this problem? q+9/2 + q-3/3=6 Thank you.1 solutions Answer 93359 by ankor@dixie-net.com(15636)   on 2008-02-17 15:21:38 (Show Source): You can put this solution on YOUR website! + = 6 We can get rid of the denominators by multiplying the equation by 6: 6* + 6* = 6(6) Cancel out the denominators and you have: 3(q+9) + 2(q-3) = 36 : 3q + 27 + 2q - 6 = 36 : 5q + 21 = 36 : 5q = 36 - 21 : 5q = 15 q = q = 3 : : Check in original equation, substitute 3 for q: + = 6 + 0 = 6; confirms our solution
 Polynomials-and-rational-expressions/127382: Solve. 3 - a-1/a+2 = a^2-1/a+2 The first number seems to throwing me off, can someone help?1 solutions Answer 93353 by ankor@dixie-net.com(15636)   on 2008-02-17 14:04:56 (Show Source): You can put this solution on YOUR website!Assume it's : : ; Added to both sides : They have the same denominators so we can just write it: = ; combine like terms, we have quadratic now That will factor to: Cancel out the (a+2)'s and we have a simple equation a - 1 = 3 : a = 3 + 1 : a = 4 : : Check solution in the original equation, substitute 4 for a 3 is equal to 18/6: ; confirms our solution of a = 4 : Could you follow what we did here? Any questions?
 Equations/127406: sally has f bags of lego in each are 22 blocks .sam has 9 lego blocks spare so gives them to sally.expression for numer of blocks sally has.sally has 119 blocks.form an equation solve the equaation find the number of lego bags sally has1 solutions Answer 93352 by ankor@dixie-net.com(15636)   on 2008-02-17 13:30:29 (Show Source): You can put this solution on YOUR website!sally has f bags of lego in each are 22 blocks .sam has 9 lego blocks spare so gives them to sally.expression for numer of blocks sally has.sally has 119 blocks.form an equation solve the equaation find the number of lego bags sally has : They have come up with a wonderful thing called "punctuation", and "capital letters". Hopefully, it will be available in your area soon. Then this problem can be much more understandable. : Rewriting, using this wonderful thing: : Sally has f bags of lego. In each are 22 blocks. Sam has 9 lego blocks to spare, so he gives them to Sally. Write an expression for number of blocks Sally has. Sally has 119 blocks. Form an equation. Solve the equation to find the number of lego bags Sally has. : An expression for the number of blocks Sally has after receiving 9 from Sam 22f + 9 : "Form an equation for the number of blocks Sally has:" 22f + 9 = 119 : "Solve the equation to find the number of lego bags, Sally has." (Find f) 22f + 9 = 119 : Subtract 9 from both sides: 22f = 119 - 9 : 22f = 110 f = ; divide both sides by 22 f = 5 bags : Check this in the equation we formed: 22(5) + 9 = 110 + 9 = 119 confirms our solution of f = 5 ; : Did this help you? Any questions?
 Linear-systems/127392: the mansfield tigers were playing the cougars on Friday Fight. Tickets wnet on sale at four o'clock on Thursday afternoon. Adult tickets sold for five dollars and student tickets cost 3.50. The total proceeds from Thursday's ticket sales were 155. if 37 tickets were sold on Thursday, how many were adult tickets and how many were adult tickets and how many were student tickets? 1 solutions Answer 93346 by ankor@dixie-net.com(15636)   on 2008-02-17 13:01:22 (Show Source): You can put this solution on YOUR website!Adult tickets sold for five dollars and student tickets cost 3.50. The total proceeds from Thursday's ticket sales were 155. if 37 tickets were sold on Thursday, how many were adult tickets and how many were adult tickets and how many were student tickets? : Let a = no. of adult tickets Let s = no. of student tickets : The ticket value\$ equation: 5a + 3.5s = 155 ; The total tickets sold equation: a + s = 37 we can also write it as: s = (37 - a) : Substitute (37-a) for s in the 1st equation: 5a + 3.5(37-a) = 155 : 5a + 129.5 - 3.5a = 155; multiplied what's inside the brackets. : 5a - 3.5a = 155 - 129.5 : 1.5a = 25.5 a = a = 17 adult tickets sold then 37 - 17 = 20 student tickets sold ; : Check solution in the \$\$ equation: 5(17) + 3.5(20) = 85 + 70 = 155; confirms our solutions : Did this make sense to you? Any questions?
 Linear_Equations_And_Systems_Word_Problems/127380: i need help with this one problem. Find three consecutive even integers such that three times the middle integer is six more than the summ of the first and third.1 solutions Answer 93333 by ankor@dixie-net.com(15636)   on 2008-02-17 11:46:13 (Show Source): You can put this solution on YOUR website!Just write an expression or equation for what it says: "Find three consecutive even integers" x, (x+2), (x+4) : " such that three times the middle integer is six more than the sum of the first and third." 3(x+2) = 6 + x + (x+4) : 3x + 6 = 2x + 10 : 3x - 2x = 10 - 6 : x = 4 is the 1st integer, then 6, 8 are the next two : : Check solution in the statement: "three times the middle integer is six more than the sum of the first and third." 3(6) = 6 + 4 + 8; confirms our solution : Not that hard, right?
 Polynomials-and-rational-expressions/127379: Add. Simplify, if possible. I think I'm getting thrown off by the exponents. Can you help me? t+x/tx^2 + 4t+x/t^2x This is supposed to be set up like fractions on either side of the addition sign. I hope that helps!1 solutions Answer 93332 by ankor@dixie-net.com(15636)   on 2008-02-17 10:39:49 (Show Source): You can put this solution on YOUR website!Assume the problem is: : The common denominator will be: So we have: = = ; about all you can do with it
 Angles/127317: the complement of an angle is 18 degrees more than 1/3 its supplement. find the measure of the angle.1 solutions Answer 93331 by ankor@dixie-net.com(15636)   on 2008-02-17 10:23:44 (Show Source): You can put this solution on YOUR website!The complement of an angle is 18 degrees more than 1/3 its supplement. find the measure of the angle. : The expression representing the complement of an angle (x): (90 - x) : The expression representing the supplement of an angle (x) (180 - x) : "the complement of an angle is 18 degrees more than 1/3 its supplement." (90 - x) = (180-x) + 18 : 90 - x = 60 - x + 18; found one third of 180 : 90 - x = 78 - x : 90 - 78 = -x + x : 12 = +x Multiply equation by 3 to get rid of the denominator 3(12) = 3*x 36 = 2x x = x = 18 degrees : : Check solution using the statement: "the complement of an angle is 18 degrees more than 1/3 its supplement." (90 - 18) = (180-18) + 18 72 = *162 + 18 72 = 54 + 18
 Percentage-and-ratio-word-problems/127343: A chemistry experiment calls for a 40% scotch whiskey solution. If your pantry has only a 30% and a 100% solution of a 12 year old scotch, how much of each should be mixed to obtain 14 liters of a 40% for your favorite drink.1 solutions Answer 93294 by ankor@dixie-net.com(15636)   on 2008-02-16 21:12:56 (Show Source): You can put this solution on YOUR website!A chemistry experiment calls for a 40% scotch whiskey solution. If your pantry has only a 30% and a 100% solution of a 12 year old scotch, how much of each should be mixed to obtain 14 liters of a 40% for your favorite drink. : Let x = 100% solution The resulting amt is given as 14 liters, therefore: (14-x) = 30% solution : a typical mixture equation: ; 1.0x + .30(14-x) = .40(14) : 1x + 4.2 - .3x = 5.6 : 1x - .3x = 5.6 - 4.2 : .7x = 1.4 x = x = 2 liters of 100% solution and 14 - 2 = 12 liters of 30% solution : : Check solutions in original equation: 1(2) + .3(12) = .4(14) 2 + 3.6 = 5.6
 Percentage-and-ratio-word-problems/127342: Player A can run the 40 yard dash in 4 seconds. Player B can run the 40 yard dash in 5 seconds. If player A cathes the football at the 20 yard line running at full speed, and player B at the 15 yard line (also at full speed) starts after player A. How long will it take player B to catch player A. On what yard line will player A be caught on?1 solutions Answer 93292 by ankor@dixie-net.com(15636)   on 2008-02-16 21:03:51 (Show Source): You can put this solution on YOUR website!Player A can run the 40 yard dash in 4 seconds. Player B can run the 40 yard dash in 5 seconds. If player A catches the football at the 20 yard line running at full speed, and player B at the 15 yard line (also at full speed) starts after player A. How long will it take player B to catch player A. On what yard line will player A be caught on? : Player B is slower than Player A; he will never catch him.
 Quadratic_Equations/127315: Miranda is making a bow for a Christmas wreath. The bow is made from six yards of ribbon which must be cut into three pieces where two pieces are the same length and the third piece is eight times as long. Find the length of each piece. I don't know where to even begin....HELP!!1 solutions Answer 93291 by ankor@dixie-net.com(15636)   on 2008-02-16 20:47:51 (Show Source): You can put this solution on YOUR website!Miranda is making a bow for a Christmas wreath. The bow is made from six yards of ribbon which must be cut into three pieces where two pieces are the same length and the third piece is eight times as long. Find the length of each piece. : Come on, it's not that hard : Let x = the length one of the small equal pieces Then 8x = the long piece : Long piece + small piece + small piece = 6 yards 8x + x + x = 6 : 10x = 6 x = x = .6 yds is the length of one of the equal pieces then 8(.6) = 4.8 yds is the length of the long piece : : Check solution: 4.8 + .6 + .6 = 6 yds
 Linear_Equations_And_Systems_Word_Problems/127340: Not sure if this came from a textbook or not. The problem has been cut and pasted onto a blank sheet of paper. The problem says: The perimeter of a rectangle is 64cm. The length of the rectangle is 2cm more than 1 and 1/2 times the width. Find the dimensions of the rectangle. Underneath this, the teacher has written: Find and write the two equations. Solve the system by graphing. Your help will be greatly appreciated.1 solutions Answer 93290 by ankor@dixie-net.com(15636)   on 2008-02-16 20:36:22 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 64cm. The length of the rectangle is 2cm more than 1 and 1/2 times the width. Find the dimensions of the rectangle. Underneath this, the teacher has written: Find and write the two equations. Solve the system by graphing. : Since we will be graphing Let x = the width Let y = the length : The 1st equation is is easy, the perimeter equation: 2x + 2y = 64 Simplify, divide equation by 2 x + y = 32 Put it in the general (y=) form for graphing y = 32 - x Plot it for x = 0 and x = 4 x | y ------- 0 |32 4 |28 : Get the 2nd equation from the statement: "The length of the rectangle is 2cm more than 1 and 1/2 times the width." y = 1.5x + 2 Plot this for x = 0 and x = 4 x | y -------- 0 | 2 4 | 8 : your graph should look like this: : With a calibrated eyeball you can see they intersect at x=12, y=20 and this is solution to the system ; You can confirm our solution by substitution in both equations 2(12) + 2(20) = 64 and 20 = 1.5(12) + 2 : Did you follow what went on here? Any questions?
 Travel_Word_Problems/127316: at 1pm your friend leaves for college traveling on the interstate at a constant speed of 65mph. at 1:24 you realize he has forgotten some necessary things for living away at college. you drive after your friend maintaining a speed of 70 mph. if neither of you alter your speed, how many miles you travel before you overtake him?1 solutions Answer 93288 by ankor@dixie-net.com(15636)   on 2008-02-16 20:19:26 (Show Source): You can put this solution on YOUR website!At 1 pm your friend leaves for college traveling on the interstate at a constant speed of 65 mph. At 1:24 pm you realize he has forgotten some necessary things for living away at college. You drive after your friend maintaining a speed of 70mph. If neither of you alter your speed, how many miles will you travel before you overtake him? : Let d = distance traveled when you catch up with your friend : Change 24 min to hrs. 24/60 = .4 hrs : When this happens, they will have traveled the same distance (d): ; Write a time equation: Time = Friends time - .4 hrs = your time - .4 = Multiply equation by 65*70 = 4550 4550* - 4550(.4) = 4550* Cancel out the denominators and you have: 70d - 1820 = 65d 70d - 65d = 1820 5d = 1820 d = d = 364 miles : That seems like a long way. Check solution by finding the travel times 364/65 = 5.6 hr 364/70 = 5.2 hr --------------- differ = 0.4 hrs; confirms our solution : : Did this make sense? Did I explain it well enough?
 Graphs/127141: An employee who produces x units per hour earns an hourly wage of y = 0.35x + 11 (in dollars). Find the hourly wage for an employee who produces 2 units per hour.1 solutions Answer 93287 by ankor@dixie-net.com(15636)   on 2008-02-16 19:38:46 (Show Source): You can put this solution on YOUR website!An employee who produces x units per hour earns an hourly wage of y = 0.35x + 11 (in dollars). Find the hourly wage for an employee who produces 2 units per hour. : Just substitute 2 for x in the equation and find y : y = .35(2) + 11 y = .70 + 11 y = \$11.70
 Mixture_Word_Problems/127260: I'm not sure if this is a mixture equation, but: The sum of the digits of a two digit number is 11. The number obtained by reversing the order of the digits is 27 less than the original number. Find the original number.1 solutions Answer 93281 by ankor@dixie-net.com(15636)   on 2008-02-16 18:58:03 (Show Source): You can put this solution on YOUR website!The sum of the digits of a two digit number is 11. The number obtained by reversing the order of the digits is 27 less than the original number. Find the original number. : Let x = the original number 10's digit Let y = the original number units digit : Write an equation for each statement: : "The sum of the digits of a two digit number is 11." x + y = 11 or y = (11 - x); will use this for substitution : "number obtained by reversing the order of the digits is 27 less than the original number." 10y + x = 10x + y - 27 : 10y - y = 10x - x - 27; some basic algebra operations : 9y = 9x - 27 : y = x - 3; simplified, divided equation by 9 : Find the original number. : Substitute (11-x) for y in the above equation 11 - x = x - 3 : 11 + 3 = x + x : 14 = 2x : x = 7 is the 10's digit then 11 - 7 = 4 is the units digit : 74 is the original number : Check solution using the statement: "number obtained by reversing the order of the digits is 27 less than the original number." 47 = 74 - 27; confirms our solution : : Could you follow what we did here? This is a good method to use on all these type of problems.
 Word_Problems_With_Coins/127309: This question is from textbook Introductory and Intermediate Algebra A man has twenty coins consisting of dimes and quarters. If the dimes were quarters and the quarters were dimes, he would have ninety cents more than he has now. How many dimes and quarters does he have?1 solutions Answer 93270 by ankor@dixie-net.com(15636)   on 2008-02-16 17:14:35 (Show Source): You can put this solution on YOUR website!A man has twenty coins consisting of dimes and quarters. If the dimes were quarters and the quarters were dimes, he would have ninety cents more than he has now. How many dimes and quarters does he have? : Let x = original number of dimes Let y = original number of quarters : Let t = total value of the coins: : Original equation .10x + .25y = t Switched equation .25x + .10y = t+.90 : From this write an equation (subtracted t from both sides): .10x + .25y = .25x + .10y - .90 : .25y - 10y = .25x - .10x - .90 : .15y = .15x - .90 : y = x - 6; divide equation .15 : or in the standard form: x - y = 6 : Add to the total coin equation: x + y = 20 x - y = 6 ------------- 2x = 26 x = x = 13 dimes, the we have 7 quarters (originally) : To check our solution: Take the switched value equation, subtract the original value equation: .25(13) + .10(7) = 3.95 .10(13) + .25(7) = 3.05 ------------------------- The difference is= .90 as given
 Polynomials-and-rational-expressions/127113: I can only get so far on this division question then I am stuck. (4x^2â-xâ+5)/(2xâ+1). I know the first number in the quotient is 2xâ however, how do I divide xâ+5 (remainder), by the divisor 2xâ+1. The answer is 2xâ-3/2;R=13/2. How do I find the fractions to solve this one1 solutions Answer 93231 by ankor@dixie-net.com(15636)   on 2008-02-16 14:33:29 (Show Source): You can put this solution on YOUR website!There is some strange symbols in your expression I assume that you mean: : : : Using long division using "......" to keep thing lined up: : ...........................2x - 3/2; (note that you have to multiply 2 by 3/2 to get 3) .............------------------ 2x + 1 | 4x^2 - x + 5 ................4x^2 -2x ....................------------- ............................-3x + 5 ............................-3x - 3/2 ...............................-------- ......................................+5 & 3/2 remainder which is 13/2 : Did this help you?
 Miscellaneous_Word_Problems/127250: Janet can shovel snow from her driveway in 65 minutes. Bill can do the same job in 50 minutes. How long would it take if they worked together? It would take _____ minutes. I've had to do a couple of similar problems using hours, but for some reason the minutes is throwing me off. Please help!1 solutions Answer 93229 by ankor@dixie-net.com(15636)   on 2008-02-16 13:04:48 (Show Source): You can put this solution on YOUR website!Janet can shovel snow from her driveway in 65 minutes. Bill can do the same job in 50 minutes. How long would it take if they worked together? : Minutes, hours, days, years, it does not matter as long as you're consistent. Don't use minutes for one person and hours for another, for example : Let t = time to complete the job working together : Let competed job = 1 : + = 1 : Multiply equation by a multiple of 65 and 50; 650 come to mind 650* + 650* = 650(1) : Cancel out the denominators and you have: 10t + 13t = 650 : 23t = 650 t = t = 28.26 minutes : : Check solution using a calc + = .9999 ~ 1