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 Age_Word_Problems/125965: Ms K is 6 years more than 3 times as old as her daughter. 8 years ago she was 2 years less than 9 times as old as her daughter was then. What are thier ages?1 solutions Answer 92313 by ankor@dixie-net.com(15653)   on 2008-02-10 11:54:17 (Show Source): You can put this solution on YOUR website!Let k = K's age now; let d = daughter's age now : Just write an equation for what it says: : "Ms K is 6 years more than 3 times as old as her daughter." k = 3d + 6 : 8 years ago they would have been (k-8) and (d-8) : "8 years ago she was 2 years less than 9 times as old as her daughter was then." (k-8) = 9(d-8) - 2 : k - 8 = 9d - 72 - 2 : k = 9d - 74 + 8 : k = 9d - 66 : What are their ages? : Substitute (3d+6) for k in the above equation, find d (3d+6) = 9d - 66 : 3d - 9d = -66 - 6 : -6d = -72 d = d = +12 yrs is the daughter's age now : Mama would be: 36 + 6 = 42 yrs old now : : Check our solutions in the statement: 8 years ago she was 2 years less than 9 times as old as her daughter was then. (42-8) = 9(12-8) - 2 34 = 9(4) - 2; confirms out solutions : Could you follow this OK? Any questions?
 Polynomials-and-rational-expressions/125926: Hi can you help me with this problem? The problem is a^2-2a / 4-2a.I need to simplify this rational expression. I think the answer is a/2 (a over 2). Can you show me the steps please. I want to know if I am doing it right.This question is not in my text book,it is a handout. Thanks so much!1 solutions Answer 92303 by ankor@dixie-net.com(15653)   on 2008-02-10 10:48:57 (Show Source): You can put this solution on YOUR website! : Factor out a in the numerator and 2 in the denominator : In the denominator, change the sign outside the brackets to change the signs inside the brackets = ; : Now we can cancel out the (a-2)'s = : note that it is negative : : Did this help you? Any questions?
 Quadratic_Equations/125617: how do you find the quadratic egaution of a quardratic parbolia? if the parbolia is grapghed for you and they just ask for the eguation.?1 solutions Answer 92282 by ankor@dixie-net.com(15653)   on 2008-02-09 21:46:15 (Show Source): You can put this solution on YOUR website!how do you find the quadratic equation of a quadratic parabola? if the parabola is graphed for you and they just ask for the equation.? : Look at the x intercepts, this is the point which the graph crosses the horizontal axis : Look at this graph: : multiply the two factors from this: (x+2)(x-5) = x^2 - 3x - 10 : The fact that the intercepts multiplied together = -10, (the y intercept) tells us the coefficient of x^2 is 1
 Quadratic_Equations/125815: Some students planned for a get-together. The budget for food was \$500. Five of the students failed to come because of the distance, and therefore the cost of food for each member increased by \$5. How many students attended the get-together?1 solutions Answer 92276 by ankor@dixie-net.com(15653)   on 2008-02-09 21:00:16 (Show Source): You can put this solution on YOUR website!Some students planned for a get-together. The budget for food was \$500. Five of the students failed to come because of the distance, and therefore the cost of food for each member increased by \$5. How many students attended the get-together? : Let x = no. of students that attended then (x+5) = no. of students anticipated to attend : The original cost per student for food: Actual cost per student: : The equation Actual cost - original cost = \$5 - = 5 : Multiply each term by x(x+5) to get rid of the denominators. cancel them & you have: 500(x+5) - 500x = 5*x(x+5) : 500x + 2500 - 500x = 5x^2 + 25x : 5x^2 + 25x - 2500 = 0; 500x's cancel, arrange as a quadratic equation : Simplify divide eq by 5: x^2 + 5x - 500 = 0 : Factors to: (x + 25) (x - 20) = 0 : Positive solution is what we want: x = +20 students actually attended ; : Check solution by finding the cost per student original 500/25 = 20 actual: 500/20 = 25 --------------------- difference cost = 5
 Expressions-with-variables/125662: Write the following as an algebraic expression then simplify a) The sum of three consecutive integers if x is the first consectutive integers. b)The perimeter of a square with side length 3x +1.1 solutions Answer 92265 by ankor@dixie-net.com(15653)   on 2008-02-09 19:44:46 (Show Source): You can put this solution on YOUR website!Write the following as an algebraic expression then simplify : a) The sum of three consecutive integers if x is the first consecutive integers. Sum = x + (x+1) + (x+2) Sum = 3x + 3 Sum = 3(x+1) : b)The perimeter of a square with side length 3x +1. P = 4(3x + 1)
 Travel_Word_Problems/125596: an air rescue plane averages 300 miles per hour in still air. It carries enough fuel for 5 hours of flying time. If, upon takeoff it encounters a head wind of 30 mi/hr and the wind remains constant, how far can the plane fly and then return safely.1 solutions Answer 92262 by ankor@dixie-net.com(15653)   on 2008-02-09 19:38:48 (Show Source): You can put this solution on YOUR website!an air rescue plane averages 300 miles per hour in still air. It carries enough fuel for 5 hours of flying time. If, upon takeoff it encounters a head wind of 30 mi/hr and the wind remains constant, how far can the plane fly and then return safely. : The outbound speed: 300 - 30 = 270 mph The return speed: 300 + 30 = 330 mph : Let d = distance to the point of no return : Write a time equation: Time = : Outbound time + return time = 5 hrs + = 5 : Multiply equation by a multiple of 270 and 330, 89100 will do it: 330d + 270d = 5(89100) : 600d = 445500 d = d = 742.5 miles max distance : However, they use the word "safely", I doubt they would exceed 700 mi from home
 Mixture_Word_Problems/125553: This problem is not in a book it is a hand out. If the mixture is P% gasoline, prices at \$1.60 per gallon, and (100-P)% alcohol, priced at \$1.00 per gallon, write a formula for the price of a gallon of gasahol.1 solutions Answer 92226 by ankor@dixie-net.com(15653)   on 2008-02-09 16:42:24 (Show Source): You can put this solution on YOUR website!This problem is not in a book it is a hand out. If the mixture is P% gasoline, prices at \$1.60 per gallon, and (100-P)% alcohol, priced at \$1.00 per gallon, write a formula for the price of a gallon of gasahol. : p = per cent gasoline : f(p) = price of a gallon of gasahol. : f(p) = + ; is the gasahol formula : : We can test our formula using 50% gasoline, it should be \$1.30 : f(50) = + f(50) = + f(50) = .80 + .50 f(50) = \$1.30
 Quadratic_Equations/125554: A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer.1 solutions Answer 92214 by ankor@dixie-net.com(15653)   on 2008-02-09 15:37:43 (Show Source): You can put this solution on YOUR website!A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer. : Looking at the first statement: "A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of row and columns, found that 24 characters were left out." : If x = number of characters in each row we translate this statement as (x*x) + 24 or x^2 + 24 = total number of characters : "When he tried to add one more row and column, he found that he was short of 25 characters." : Now, the number of rows is "x + 1", and the number of columns is "x + 1", so we have (x + 1)(x + 1) - 25 = total number of characters. : FOIL above and make it equal to the 1st equation: : x^2 + 2x + 1 - 25 = x^2 + 24 : x^2 + 2x - 24 = x^2 + 24 : x^2 - x^2 + 2x - 24 - 24 = 0 : 2x - 48 = 0 : 2x = +48 : x = 48/2 : x = 24 : : Grid is 24 by 24 which contains 576 character + 24 left out = 600 : Grid of 25 by 25 = 625 character so he would have 25 blanks : Did this make sense? Hope so.
 Polynomials-and-rational-expressions/125759: Can you PLEASE help me out with a few problems? I can not figure them out to save my life. Thank you in advance!! Solve. 1) x squared-3x OVER 5x squared TIMES 10x OVER x squared-4x+3 Solve. 2) 5 OVER x MINUS x-3 OVER x+2 = 22 OVER x squared +2x 1 solutions Answer 92202 by ankor@dixie-net.com(15653)   on 2008-02-09 13:54:54 (Show Source): You can put this solution on YOUR website!1) x squared-3x OVER 5x squared TIMES 10x OVER x squared-4x+3 * : * ; canceled 5x into 10x : (x-3) * ; canceled out x : ; canceled out (x-3) : : Solve. 2) 5 OVER x MINUS x-3 OVER x+2 = 22 OVER x squared + 2x - = : - = : Multiply equation by x(x+2) x(x+2)* - x(x+2)* = x(x+2)* Cancel out the denominators and you have: : 5(x+2) - x(x-3) = 22 : 5x + 10 - x^2 + 3x = 22; multiplied what's inside the brackets : 5x + 3x - x^2 + 10 - 22 = 0 : -x^2 + 8x - 12 = 0 : This is easier to factor if we change the signs, multiiply by -1 x^2 - 8x + 12 = 0 factors to: (x-6)(x-2) = 0 x = +6 x = +2 : : You can check both solutions in the original equation to confirm they are correct.
 Rate-of-work-word-problems/125606: a new machine can make 10000 cans three times faster than an older one. With both machines working ,10000 cans can be made in 9 hrs. How long would it take the new machine, working alone to make 10000 cans?1 solutions Answer 92193 by ankor@dixie-net.com(15653)   on 2008-02-09 12:53:34 (Show Source): You can put this solution on YOUR website!a new machine can make 10000 cans three times faster than an older one. With both machines working ,10000 cans can be made in 9 hrs. How long would it take the new machine, working alone to make 10000 cans? : Let x = time for the new machine to do the job by itself then 3x = time required for the old machine to do the job by itself, (take 3 times as long) : Let the completed job = 1; (the making of 10,000 cans) : + = 1 : Multiply equation to get rid of the denominators and you have: 9 + 3(9) = 3x : 9 + 27 = 3x : 36 = 3x x = x = 12 hrs, new machine working by itself : Check solution in original equation (old machine time 3*12 = 36hrs) + = 1 + = 1
 Polynomials-and-rational-expressions/125808: This question is from textbook Introductory Algebra If anyone could help me with this problem, it would be greatly appreciated. The problem reads: A polynomial in x has degree 3. The coefficient of x^2 is 3 less than the coefficient of x^3. The coefficient of x is three times the coefficient of x^2. The remaining coefficient is 2 more than the coefficient of x^3. The sum of the coefficient is -4. Find the polynomial.1 solutions Answer 92191 by ankor@dixie-net.com(15653)   on 2008-02-09 12:27:36 (Show Source): You can put this solution on YOUR website! The problem reads: "A polynomial in x has degree 3." Write it: ax^3 + bx^2 + cx + d : The coefficient of x^2 is 3 less than the coefficient of x^3. b = a - 3 : The coefficient of x is three times the coefficient of x^2. c = 3b also, substituting (a-3) for b c = 3(a-3) c = 3a - 9 : The remaining coefficient is 2 more than the coefficient of x^3. d = a + 2 : The sum of the coefficient is -4. a + b + c + d =-4 : Using the 1st 3 equations, substitute for b, c, d: a + (a-3) + (3a-9) + (a+2) = -4 a + a - 3 + 3a - 9 + a + 2 = -4 we gather together: a + a + 3a + a - 3 - 9 + 2 = - 4 6a - 10 = -4 6a = -4 + 10 6a = 6 a = 1 Then using the 1st 3 equations, substituting 1 for a b = 1 - 3 b = -2 and c = 3(1) - 9 c = -6 and d = 1 + 2 d = 3 : Find the polynomial. : y = x^2 - 2x^2 - 6x + 3
 Mixture_Word_Problems/125803: Kevin is three times as old as Bob. Three years ago the sum of their ages was 22yr. How old is each now? 1 solutions Answer 92184 by ankor@dixie-net.com(15653)   on 2008-02-09 11:15:41 (Show Source): You can put this solution on YOUR website!Write an equation for each statement: : "Kevin is three times as old as Bob." k = 3b : Three years ago, their ages; (k-3) and (b-3), right? : "Three years ago the sum of their ages was 22yr." (k-3) + (b-3) = 22 : k - 3 + b - 3 = 22 : k + b - 6 = 22 : k + b = 22 + 6 : k + b = 28 : How old is each now? : Substitute 3b for k, find b 3b + b = 28 : 4b = 28 b = b = 7 yrs old is Bob then 3(7) = 21 yrs old is Kevin : : Check our solution using the statement: "Three years ago the sum of their ages was 22yr. " (21-3) + (7-3) = 18 + 4 = 22; confirms our solution : Not that hard, do you think?
 Mixture_Word_Problems/125802: Two cars start from towns 400 mi apart and travel toward each other. They meet after 4 hrs. Find the speed of each car if one travels 20mph faster than the other.1 solutions Answer 92183 by ankor@dixie-net.com(15653)   on 2008-02-09 11:06:15 (Show Source): You can put this solution on YOUR website!Two cars start from towns 400 mi apart and travel toward each other. They meet after 4 hrs. Find the speed of each car if one travels 20mph faster than the other. : Let s = speed of the slower car then (s+20) = speed of the faster : When they meet, we know they will have traveled a total of 400 mi. : Make a distance equation: Distance = time * speed : Slow car dist + fast car dist = 400 miles 4s + 4(s+20) = 400 : 4s + 4s + 80 = 400 : 8x = 400 - 80 s = s = 40 mph is the slow car and 60 mph is the fast car : : We can check our solution by finding the total distance: 4(40) + 4(60) = 400
 logarithm/125792: I don't know how to type something for exponent don't know how to type it because i have some things like 10 exponent 1-2lg10 (note 1-2lg10 is the exponent)1 solutions Answer 92182 by ankor@dixie-net.com(15653)   on 2008-02-09 10:57:07 (Show Source): You can put this solution on YOUR website!10 exponent 1-2lg10 (note 1-2lg10 is the exponent) : Assume you mean: : We know log of 10 is 1 : : =
 Mixture_Word_Problems/125804: A table is three times as long as it is wide. If it were 3 ft shorter and 3 ft wider, it would be square (with all sides equal). How long and how wide is the table?1 solutions Answer 92180 by ankor@dixie-net.com(15653)   on 2008-02-09 10:47:07 (Show Source): You can put this solution on YOUR website!A table is three times as long as it is wide. If it were 3 ft shorter and 3 ft wider, it would be square (with all sides equal). How long and how wide is the table? : Let x = original width then 3x = original length : If length is increased by 3 and the width is decreased by 3,it is square, therefore: (3x - 3) = (x + 3) 3x -x = 3 + 3 2x = 6 x = 3 is the width, therefore length: 3*3 = 9
 Equations/125307: This question is from textbook algebra: structure and method: book1 Ingrid can rake our lawn in 90 min ad I can do it in 60 min. If she rakes for 15 min before I join her, how long will it take us to finish? PLEASE HELP!!! The answer is 30 min, but I don't know how to get there. HELP IS MUCH APPRICIATED!!!!!!!!!1 solutions Answer 92179 by ankor@dixie-net.com(15653)   on 2008-02-09 10:12:31 (Show Source): You can put this solution on YOUR website!Ingrid can rake our lawn in 90 min and I can do it in 60 min. If she rakes for 15 min before I join her, how long will it take us to finish? : Let x = time (in min) for you to finish the job : Let the completed job = 1 : + + = 1 : Multiply equation by 180 to get rid of the denominators: 180* + 180* + 180* = 180(1) Cancel the denominators and you have: : 2(15) + 2x + 3x = 180 : 30 + 2x + 3x = 180 : 2x + 3x = 180 - 30 : 5x = 150 x = x = 30 min
 Linear_Equations_And_Systems_Word_Problems/125540: The measure of the supplement of an angle is 4 times the measure of its complement. Find the measure of the angle.1 solutions Answer 92148 by ankor@dixie-net.com(15653)   on 2008-02-08 21:43:24 (Show Source): You can put this solution on YOUR website!: Let x = the angle : The supplement: (180-x) The complement: (90-x) : write what it says: "The measure of the supplement of an angle is 4 times the measure of its complement." (180-x) = 4(90-x) : 180 - x = 360 - 4x : -x +4x = 360 - 180 : 3x = 180 x = x = 60 is the angle : : Check solution in the original equation: (180-60) = 4(90-60) 120 = 4(30); confirms our solution
 Travel_Word_Problems/125513: a boat goes upstream 30 miles and downstream 44 miles in 10 hours.the next day it goes upstream 40 miles and downstream 55 miles in 13 hours.what is the average speed of the boat and the stream?1 solutions Answer 92141 by ankor@dixie-net.com(15653)   on 2008-02-08 21:20:15 (Show Source): You can put this solution on YOUR website!a boat goes upstream 30 miles and downstream 44 miles in 10 hours.the next day it goes upstream 40 miles and downstream 55 miles in 13 hours.what is the average speed of the boat and the stream? : Let x = speed of the boat in still water Let y = speed of the current: then (x-y) = speed upstream (x+y) = speed downstream : Write a time equation for the 1st trip: time = : Time upstream + time down stream = 10 hrs + = 10 : Do the same for the second trip: + = 13 : We can use elimination; multiply the 1st eq by 4, and the 2nd eq by 3: + = 40 + = 39 ---------------------------subtraction eliminates leaving us with = 1 which is: x + y = 11 : We can replace(x+y) with 11 in the 1st trip equation + = 10 + 4 = 10 = 10 - 4 = 6 Cross multiply 6(x-y) = 30 x - y = 5; divided equation by 6 : Using these two simple equation eliminate y x + y = 11 x - y = 5 -------------adding eliminates y 2x = 16 x = 8 mph is the boat in still water then 8 + y = 11 y = 3 mph is the current : : Check our solution in the 2nd trip equation: + = 13 : : Seems like there should be a simpler way, but I can't seem to come up with tonight.
 Percentage-and-ratio-word-problems/125456: Can someone please help me with this problem? If the population of a town is currently 350,000 and increasing at a rate of 3.25% each year, approximately when will the population reach 1,000,000 assuming it maintains this steady rate of growth? My answer options are: a.33.8 yrs b.3.73 yrs c.32.8 yrs d.17.5 yrs Please get back to me as soon as possible, I am homeschooled but on a deadline to get this finished, thanks!!!!1 solutions Answer 92127 by ankor@dixie-net.com(15653)   on 2008-02-08 19:31:42 (Show Source): You can put this solution on YOUR website!If the population of a town is currently 350,000 and increasing at a rate of 3.25% each year, approximately when will the population reach 1,000,000 assuming it maintains this steady rate of growth? : Let t = no. of years for this to occur : We know the population in 1 yr, we can multiply 350,000 by 1.0325, therefore, the equation will be: : 350000*(1.0325)^t = 1000000 : Divide both sides by 350000 1.0325^t = 1.0325^t = 2.857 : Use the nat log of both sides: ln(1.0325^t) = ln(2.857) : The log equivalent of exponents: t * ln(1.0325) = ln(2.857) : Find the nat log of both sides: .03198t = 1.04977 t = t = 32.8258 ~ 32.8 : : Check solution on a good calc; enter 350000 * l.0325^32.8 = 999222 ~ 1000000 : You can try the other solutions and see which one is closest to 1,000,000 ~
 Linear_Equations_And_Systems_Word_Problems/125537: Kelly has a purse full of quarters and dimes. There are 58 more quaters than dimes and the total value of the change is \$19.05. How many dimes are there?1 solutions Answer 92032 by ankor@dixie-net.com(15653)   on 2008-02-07 21:51:55 (Show Source): You can put this solution on YOUR website!Kelly has a purse full of quarters and dimes. There are 58 more quaters than dimes and the total value of the change is \$19.05. How many dimes are there? : Let x = no. of dimes then (x+58) = no. of quarters : .10x + .25(x+58) = 19.05 : .10x + .25x + 14.5 = 19.05 : .35x = 19.05 - 14.5 : .35x = 4.55 x = x = 13 dimes : : Find the number of quarters and check the solution: 13 + 58 = 71 quarters .10(13) + .25(71) = 1.30 + 17.75 = 19.05