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 Numbers_Word_Problems/319415: find a number that is twice its square root,increased by 7 is 91 solutions Answer 228756 by ankor@dixie-net.com(15652)   on 2010-07-03 08:23:27 (Show Source): You can put this solution on YOUR website!find a number that is twice its square root,increased by 7 is 9 : + 7 = 9 : = 9 - 7 = 2 square both sides 4x = 4 x = 1 : Check solution in original equation + 7 = 9 2(1) + 7 = 9
 Evaluation_Word_Problems/319127: Tim has \$5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer. He has fice more nickles than quarters, then number of pennies is two-thirds the number of nickles, there are half as many half-dollars as pennies, and half as many dimes as nickels. How many coins of each type does he have? 1 solutions Answer 228723 by ankor@dixie-net.com(15652)   on 2010-07-02 21:47:25 (Show Source): You can put this solution on YOUR website!Tim has \$5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer. He has five more nickles than quarters, then number of pennies is two-thirds the number of nickles, there are half as many half-dollars as pennies, and half as many dimes as nickels. How many coins of each type does he have? : Write a equation for each statement: "Tim has \$5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer." .01p + .05n + .10d + .25q + .50h = 5.03 : "He has five more nickles than quarters," n = q + 5 or q = n - 5 : "then number of pennies is two-thirds the number of nickles," p = n : "there are half as many half-dollars as pennies," h = p replace p with n h = *n h = n : " half as many dimes as nickels." d = .5n : .01p + .05n + .10d + .25q + .50h = 5.03 get rid of the decimals, multiply by 100 p + 5n + 10d + 25q + 50 = 503 Get everything in terms of n, replace p, d, q, and h n + 5n + 10(.5n) + 25(n-5) + 50*n = 503 multiply by 3, get rid of the fractions 2n + 15n + 30(.5n) + 75(n-5) + 50n = 1509 : 2n + 15n + 15n + 75n - 375 + 50n = 1509 : 157n = 1509 + 375 : 157n = 1884 n = n = 12 nickels : How many coins of each type does he have? p:*12 = 8 pennies : h: *12 = 4 half dollars : q: 12 - 5 = 7 quarters : d: .5(12) = 6 dimes : : Check the solutions, find the total .01(8) + .05(12) + .10(6) .25(7) + .50(4) = .08 + .60 + .60 + 1.75 + 2.00 = 5.03; confirms our solutions
 Quadratic_Equations/319350: Type an exact answer using radicals as needed and use commas to separate answers. What is the solution? w = w^4 - 2w^2 - 2 = 01 solutions Answer 228715 by ankor@dixie-net.com(15652)   on 2010-07-02 20:14:17 (Show Source): You can put this solution on YOUR website!w^4 - 2w^2 - 2 = 0 : Find w^2 using the quadratic formula in this equation x=w^2, a=1, b=-2, c=-2 : : Two solutions extract the sqrt of 4 Cancel the 2's Find the square root of both sides w = ; a good solution : but we also have extract the sqrt of 4 Cancel the 2's Find the square root of both sides w = However sqrt of 3 > 1, therefore we have square root of a neg number : I'm going to say the exact solution using radicals w = +, - : Confirm this with a graph of this equation
 Polynomials-and-rational-expressions/319348: The base of a triangle is 4 inches less than twice the height. The area is 35 inches^2. Find the height and the base. Please help me with this problem. Thank you.1 solutions Answer 228679 by ankor@dixie-net.com(15652)   on 2010-07-02 16:44:00 (Show Source): You can put this solution on YOUR website!The base of a triangle is 4 inches less than twice the height. The area is 35 inches^2. Find the height and the base. : Let x = the height then (2x-4) = the base : The area: *(2x-4)*x = 35 Multiply both sides by 2, get rid of the fraction 2x^2 - 4x = 2(35) Arrange as a quadratic equation: 2x^2 - 4x - 70 = 0 simplify, divide by 2 x^2 - 2x - 35 = 0 Factors to (x-7)(x+5) = 0 The positive solution x = 7 in is the height then 2(7) - 4 = 10 in is the base : : Check the area with these values .5 * 7 * 10 = 35
 Volume/319271: A factory needs a box that has a volume of 6 cubic inches. The width should be 1 inch less than the height and the length should be 3 inches greater than the height. what should the dimensions of the box be?1 solutions Answer 228671 by ankor@dixie-net.com(15652)   on 2010-07-02 16:17:06 (Show Source): You can put this solution on YOUR website!A factory needs a box that has a volume of 6 cubic inches. The width should be 1 inch less than the height and the length should be 3 inches greater than the height. what should the dimensions of the box be? : Let x = the height of the box then "width should be 1 inch less than the height" (x-1) = the width of the box and "length should be 3 inches greater than the height." (x+3) = the length of the box : Volume equation x*(x-1)*(x+3) = 6 x(x^2 + 2x - 3) = 6 x^3 + 2x^2 - 3x = 6 x^3 + 2x^2 - 3x - 6 = 0: graph this to find the positive solution x = 1.732 is the height then .732 = the width and 4.732 = the length ; : Check solution: 4.732*.732*1.732 = 5.999 ~ 6
 Polynomials-and-rational-expressions/318982: Will someone please help me with these problems. 1) Factors: -8t+xt-24x+3x^2 2) Factors: 9t+wt+9y+yw 3) factors: 5x^2+13xy-6y^2 4) Factor: tu-24t+3t^2-8u1 solutions Answer 228668 by ankor@dixie-net.com(15652)   on 2010-07-02 15:50:05 (Show Source): You can put this solution on YOUR website!1) Factors: -8t+xt-24x+3x^2 Group the terms as follows xt + 3x^2 - 8t - 24x factor out x and -8 x(t+3x) - 8(t+3x); a -8 changes the sign Factor out (t+3x) (t+3x)(x-8) : 2) Factors: 9t+wt+9y+yw Group as follows 9t + 9y + wt + yw Factor out 9 & w 9(t+y) + w(t+y) Factor out (t+y) (t+y)(9+w) : 3) factors: 5x^2+13xy-6y^2 This can be factored as a quadratic, we know that it will be: (5x___y)(x___y) The factors of 6 are 2 & 3, choose the signs to satisfy the middle term 13xy (5x - 2y)(x + 3y); FOIL this to check it : 4) Factor: tu-24t+3t^2-8u This is very similar to the 1st problem See if you can do this exactly the same way
 Quadratic_Equations/319338: how can you determine the nature of roots of this following equation: the square root of 3x suared minus 4 suare roots of 3 equals 0?1 solutions Answer 228659 by ankor@dixie-net.com(15652)   on 2010-07-02 15:00:50 (Show Source): You can put this solution on YOUR website! the square root of 3x squared minus 4 square roots of 3 equals 0? = 0 add to both sides : Square both sides 3x^2 = 16(3) Divide both sides by 3 x^2 = 16 x = x = 4 : : Check solution in original equation = 0 extract the square root = 0
 Percentage-and-ratio-word-problems/319332: On an exam with q questions, Marie correctly answered 15 of the first 20 but just 1/3 of the rest. If her total score was 50%, what was q?1 solutions Answer 228654 by ankor@dixie-net.com(15652)   on 2010-07-02 14:32:59 (Show Source): You can put this solution on YOUR website!On an exam with q questions, Marie correctly answered 15 of the first 20 but just 1/3 of the rest. If her total score was 50%, what was q? : .50q = 15 + (q-20) Multiply equation by 3, to get rid of the fraction, results: 3(.5q) = 3(15) + q - 20 : 1.5q - q = 45 - 20 : .5q = 25 Multiply both sides by 2 q = 50 : : Check solution 15 + 1/3(50 - 20) = 15 + 10 = 25 which is 50% of 50
 Travel_Word_Problems/319190: Samia walks for a time at 4mph, then slows down and walks at 3.2mph. The total distance she walked was 6 miles. If she walked for 0.5 hour more at 3.2 mph than she did at 4mph, determine the time Samia walked at 4mph.1 solutions Answer 228566 by ankor@dixie-net.com(15652)   on 2010-07-01 22:01:12 (Show Source): You can put this solution on YOUR website!Samia walks for a time at 4mph, then slows down and walks at 3.2mph. The total distance she walked was 6 miles. If she walked for 0.5 hour more at 3.2 mph than she did at 4mph, determine the time Samia walked at 4mph. : Let t = time walked at 4 mph then (t+.5) = time walked at 3.2 mph : Write a distance equation: dist = speed * time : dist at 4 + dist at 3.2 = 6 miles 4t + 3.2(t+.5) = 6 : 4t + 3.2t + 1.6 = 6 : 7.2t = 6 - 1.6 ; 7.2t = 4.4 t = t = .611 hrs at 4 mph and .611 + .5 = 1.111 hrs at 3.2 mph : : Check solution by finding the distances .611 * 4 = 2.44 mi 1.11 * 3.2 = 3.55 mi ---------------------- total dist: 5.99 ~ 6 mi
 Quadratic_Equations/319191: if you drop an object from 1936 feet, how long until it hits the ground?1 solutions Answer 228564 by ankor@dixie-net.com(15652)   on 2010-07-01 21:50:37 (Show Source): You can put this solution on YOUR website!if you drop an object from 1936 feet, how long until it hits the ground? Let t = time in seconds : -16t^2 + 1936 = 0 : -16t^2 = -1936 Divide both sides by -16 t^2 = 121 t = t = 11 sec
 Pythagorean-theorem/319180: 15 squared + b squared= 22 squared1 solutions Answer 228560 by ankor@dixie-net.com(15652)   on 2010-07-01 21:24:52 (Show Source): You can put this solution on YOUR website! : : : : b = b ~ 16.09
 Travel_Word_Problems/318875: During the first part of a trip a canoeist travels 49 miles at a certain speed. The canoeist travels 6 miles on the second part of the trip at a speed of 5mph slower. The total time for the trip is 3hrs. What was the speed on each part of the trip?1 solutions Answer 228555 by ankor@dixie-net.com(15652)   on 2010-07-01 21:17:18 (Show Source): You can put this solution on YOUR website!During the first part of a trip a canoeist travels 49 miles at a certain speed. The canoeist travels 6 miles on the second part of the trip at a speed of 5mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip? : Let s = speed traveled the 1st 49 mi then (s-5) = speed on the last 6 mi : Write a time equation: time = dist/speed : time for 49 mi + time for 6 mi = 3 hrs + = 3 multiply by s(s-5), results: 49(s-5) + 6s = 3s(s-5} 49s - 245 + 6s = 3s^2 - 15s 55s - 245 = 3s^2 - 15s 0 = 3s^2 - 15s - 55s + 245 3s^2 - 70s + 245 = 0 : Solve for s using the quadratic formula; only one solution will make sense
 Complex_Numbers/318851: If it takes 2 men to do a job in 12 hours, how many men will it take to do the same job in 30 minutes?1 solutions Answer 228315 by ankor@dixie-net.com(15652)   on 2010-06-30 20:24:18 (Show Source): You can put this solution on YOUR website!If it takes 2 men to do a job in 12 hours, how many men will it take to do the same job in 30 minutes? : We can use man-hours here : 2 * 12 = 24 man-hours to do the job : Let m = no. of men to do the same job in 30 min (.5 hr) .5m = 24 m = 48 men to do the job in 30 min
 Travel_Word_Problems/318817: If I'm going somewhere that is 0.8 miles away and is approximately a 1 minute drive, how long would it take to walk at a normal pace? Obviously longer than the one minute it would to drive, but I'd like to know.1 solutions Answer 228289 by ankor@dixie-net.com(15652)   on 2010-06-30 19:12:25 (Show Source): You can put this solution on YOUR website!If I'm going somewhere that is 0.8 miles away and is approximately a 1 minute drive, how long would it take to walk at a normal pace? : If you consider a normal pace as 3 mph (that's 1 mi in 20 min, not really fast) : = .267 hrs or .267(60) = 16 min to go .8 mi
 Quadratic_Equations/318665: word problem from chapter on quadratic equations: Pipe A can fill a tank in 4 hrs. If pipe B works alone, it takes 3 hrs longer to fill the tank than if both pipes work together. How long will it take for pipe B to fill the tank if it works alone?1 solutions Answer 228288 by ankor@dixie-net.com(15652)   on 2010-06-30 19:05:44 (Show Source): You can put this solution on YOUR website! Pipe A can fill a tank in 4 hrs. If pipe B works alone, it takes 3 hrs longer to fill the tank than if both pipes work together. How long will it take for pipe B to fill the tank if it works alone? ; Let b = time required by pipe B working alone then (b-3) = time required when A & B are working together : Let the completed job = 1 (a full tank) : A shared work equation + = 1 multiply by 4b, results: b(b-3) + 4(b-3) = 4b : b^2 - 3b + 4b - 12 = 4b Arrange as a quadratic equation b^2 - 3b + 4b - 4b - 12 = 0 : b^2 - 3b - 12 = 0 Use the quadratic formula to find b in this equation, x=b; a=1; b=-3; c=-12 : : the positive solution is what we want here b = b = 5.275 hrs is the time for B to fill the pool alone : : see if that's true, (2.275 hrs for both working together) + = .56875 + .43128 = 1.000; confirms our solution
 Human-and-algebraic-language/318363: Greetings, Francois went 36 miles downstream and returned. The round trip took 5+1/4 (5.25) hours. Find the speed of the boat in still water and the speed of the current if the speed of the current is 1/7 the speed of the boat. Thank you in advance for any assistance, have a great week!1 solutions Answer 228007 by ankor@dixie-net.com(15652)   on 2010-06-29 13:47:36 (Show Source): You can put this solution on YOUR website!Francois went 36 miles downstream and returned. The round trip took 5+1/4 (5.25) hours. Find the speed of the boat in still water and the speed of the current if the speed of the current is 1/7 the speed of the boat. : Let s = speed of boat in still water then s = speed of the current : The current is added and subtracted from the boat speed so we can say: s = speed downstream and s = speed upstream : Write a time equation, time = dist/speed + = 5.25 invert the dividing fractions and multiply + = 5.25 : + = 5.25 multiply by 24s to eliminate the denominators 4(252) + 3(252) = 5.25(24s) : 1008 + 756 = 126s : s = s = 14 mph is the speed of the boat in still water then *14 = 2 mph is speed of the current : : See if this is true 36/16 + 36/12 = 2.25 + 3 = 5.25 hrs; confirms our solutions
 Human-and-algebraic-language/318479: seven times a number plus the sum of three and twice a number is 301 solutions Answer 227997 by ankor@dixie-net.com(15652)   on 2010-06-29 13:14:05 (Show Source): You can put this solution on YOUR website!just write an equation for what it says: : seven times a number plus the sum of three and twice a number is 30 7x + (3 + 2x) = 30
 Travel_Word_Problems/318285: Two cars leave City A at the same time to travel to City B. One car travels at 72 km/h and other at 78 km/h. If the slower car arrives 20 min. after the faster car, how far apart are City A and City B?1 solutions Answer 227938 by ankor@dixie-net.com(15652)   on 2010-06-29 08:39:33 (Show Source): You can put this solution on YOUR website!Two cars leave City A at the same time to travel to City B. One car travels at 72 km/h and other at 78 km/h. If the slower car arrives 20 min after the faster car, how far apart are City A and City B? : Let d = distance from City A, to City B : Change 20 min to hr : slow car time - fast car time = 20 min - = Multiply equation by 5616 (78*72), results 78d - 72d = 1872 : 6d = 5616 : d = d = 312 mi ; : Check solution - = - =
 Linear-equations/318225: Please help! I need help with two problems. I have been working on these for 2 hours now and I am lost??? 5[5m-(m+8)]>-4(m-1) graph the system of inequalities x<=2 y>=-2x+3 Thank You so much in advance!1 solutions Answer 227899 by ankor@dixie-net.com(15652)   on 2010-06-28 21:15:10 (Show Source): You can put this solution on YOUR website!5[5m-(m+8)]>-4(m-1) : 5(5m - m - 8) > -4m + 4 : 5(4m - 8) > -4m + 4 : 20m - 40 > -4m + 4 : 20m + 4m > 4 + 40 : 24m > 44 m = m = graph the system of inequalities x<=2 y>=-2x+3 : Shade the area at and to the left of x=2 (green) and at and above the red line
 Sequences-and-series/318351: If x and y are two consecutive terms in the Fibonacci sequence, how would I write an expression for the next term?1 solutions Answer 227884 by ankor@dixie-net.com(15652)   on 2010-06-28 19:47:41 (Show Source): You can put this solution on YOUR website!If x and y are two consecutive terms in the Fibonacci sequence, how would I write an expression for the next term? : f = x+y
 Travel_Word_Problems/318312: On a road trip they drove 55 miles per hour to California, on the way home they drove 65 miles per hour. How many miles did they drive on the way to California if the round trip took 10 hours? I know it's D = RxT, so I plug in 55 and 65 as rate and is time 60?...I'm totally lost...1 solutions Answer 227824 by ankor@dixie-net.com(15652)   on 2010-06-28 15:32:59 (Show Source): You can put this solution on YOUR website!On a road trip they drove 55 miles per hour to California, on the way home they drove 65 miles per hour. How many miles did they drive on the way to California if the round trip took 10 hours? : Let d = one way distance to Calif : Write a time equation, Time = dist/speed To time + return time = 10 hrs + = 10 multiply equation by (55*65), solve for d
 Equations/318247: I am working on an assignment and can not figure out the following problems can you show me how to get the correct answers? 1. (32x^3-48x^2-56x-12)/ (8x+4) 2.I have to convert this to a decimal notation and am not sure how to go about it 10^-3 3.r^2+15r=0 I am looking for the solution to r how would I find it? 4. factor by grouping gives me trouble could you show me how to do it? 3x^3-24x^2-5x+40 5.(r-45+7)+(5r+3s)+s+2)1 solutions Answer 227812 by ankor@dixie-net.com(15652)   on 2010-06-28 14:38:20 (Show Source): You can put this solution on YOUR website!1. Factor out 4 cancel the 4's using long division: ------ _________________________ (2x+1)| 8x^3 - 12x^2 - 14x - 3 you will get quotient of: 4x^2 - 8x - 3 : : 2.I have to convert this to a decimal notation and am not sure how to go about it 10^-3 = .001; prove this on your calc; enter 10^-3 : 3.r^2+15r = 0 I am looking for the solution to r how would I find it? Factor out r r(r + 15) = 0 two solutions r = 0 r = -15 : : 4. factor by grouping gives me trouble could you show me how to do it? 3x^3-24x^2-5x+40 Factor out 3x^2 on the 1st two terms, factor out 5 on the last two terms Note when you factor out -5, it makes it a MINUS 8 3x^2(x-8) - 5(x-8) Factor out (x-8) from each term; you are left with: (x-8)(3x^2 - 5) : ; 5.(r-45+7)+(5r+3s)+(s+2) plus in front of the brackets so just remove them: r-45+7+5r+3s+s+2 Group like terms r + 5r + 3s + s - 45 + 7 + 2 6r + 4s - 36 Factor out 2 2(3r + 2s - 18)
 Linear-equations/317915: I need help finding the slope and y-intercept for 1. x + 2y = 3 1 solutions Answer 227722 by ankor@dixie-net.com(15652)   on 2010-06-27 20:23:04 (Show Source): You can put this solution on YOUR website!1. x + 2y = 3 : Subtract x from both sides 2y = -x + 3 : divide both sides by 2 y = x + : slope is -, y intercept is
 Linear-equations/317918: I need to convert this problem to standard form using only integers x/8 = -4y/5 (the slash sign means over not divided into) (need this converted to standard form (using integers only)1 solutions Answer 227718 by ankor@dixie-net.com(15652)   on 2010-06-27 20:17:39 (Show Source): You can put this solution on YOUR website!x/8 = -4y/5 (the slash sign means over not divided into) : = Cross multiply 5x = 8(-4y) : 5x = -32y : 5x + 32y = 0
 Linear-equations/317852: Determine "k" so that the line through (k+2,k) and (3,2) has slope 3. 1 solutions Answer 227707 by ankor@dixie-net.com(15652)   on 2010-06-27 19:00:10 (Show Source): You can put this solution on YOUR website!Determine "k" so that the line through (k+2,k) and (3,2) has slope 3. : The slope formula: = m Assign the values as follows: x1 = (k+2) y = k x2 = 3; y2 = 2 m = 3 : = 3 : = 3 : = 3 2 - k = 3(1 - k) : 2 - k = 3 - 3k : -k + 3k = 3 - 2 : 2k = 1 : k = , or .5 : : Check the slope = = 3
 Numbers_Word_Problems/317888: you are given a two -digit positive integer. if you reverse the digits of your number . the result is a number which is 20% larger than your number . what is your number ?1 solutions Answer 227689 by ankor@dixie-net.com(15652)   on 2010-06-27 18:17:21 (Show Source): You can put this solution on YOUR website!you are given a two -digit positive integer. 10x + y = "a two digit number : if you reverse the digits of your number, the result is a number 20% larger than your number. 10y + x = 1.2(10x+y) : 10y + x = 12x + 1.2y : 10y - 1.2y = 12x - x : 8.8y = 11x : Simplify, divide both sides by 11 .8y = x : y = y = 1.25x the only single digit integer that satisfies this x = 4, y = 5 : 45 is the two digit number : : Check 1.2(45) = 54
 Equations/317731: Simplify: -x+2 2 -------- + ----- x^2-5x+6 3-x1 solutions Answer 227589 by ankor@dixie-net.com(15652)   on 2010-06-26 21:52:43 (Show Source): You can put this solution on YOUR website!Simplify: : + : + = + ; canceled the -1 Cancel (x-2)'s + =
 Linear_Equations_And_Systems_Word_Problems/317630: A farmer has 100 animals consisting of cows, pigs and chickens. He takes the animals to market and sells all of them for \$100. He sells cows for \$10 He sells pigs for \$3 He sells chickens 2 for \$1 How many of each animal does he sell? (no 1/2 animals) I came up with x+y+z=100 animals... and 10x+3y+0.5z=100 dollars I believe this needs another equation but I cannot figure it out. Also we are working with arbitrary numbers in class. Thank You! Scott M.1 solutions Answer 227584 by ankor@dixie-net.com(15652)   on 2010-06-26 21:32:49 (Show Source): You can put this solution on YOUR website!Cows cost \$10, Pigs cost \$3, and chickens cost \$.50. He only bought 100 animals and bought at least one of each animal. He only spent \$100. How many of each animal did he buy? : Let c = no. of cows; p = no. of pigs; s = no. chickens : No. of animals equation: c + p + s = 100 : Cows cost \$10, Pigs cost \$3, and chickens cost \$.50. the \$\$ equation: 10c + 3p + .5s = 100 : We have two equations but 3 unknowns, however, we know there can't very many cows, After trying a couple values for no. of cows, came up with 5 cows, they're worth \$50, our two equations then are: : p + s = 100 - 5 p + s = 95 and 3p + .5s = 100 - 50 3p + .5s = 50 : Multiply the 1st equation by 3 and subtract the 2nd equation: 3p + 3s = 285 3p + .5s = 50 ---------------- subtracting eliminates p 0p + 2.5s = 235 s = s = 94 chickens : Find pigs p + 94 = 95 p = 95 - 94 p = 1 pig : We have then: 5 cows, 1 pig, 94 chicken ; ; Check in the cost equation 10(5) + 3(1) + 94(.5) = 50 + 3 + 47 = \$100
 Age_Word_Problems/317180: Jill's present age is three times her sister's age two years ago. If Jill is 18 years old, how old is her sister now?1 solutions Answer 227226 by ankor@dixie-net.com(15652)   on 2010-06-24 21:53:05 (Show Source): You can put this solution on YOUR website!Jill's present age is three times her sister's age two years ago. j = 3(s-2) j = 3s - 6 : If Jill is 18 years old, how old is her sister now? Replace j in the above equation with 18 18 = 3s - 6 18 + 6 = 3s 24 = 3s s = s = 8 yrs sister now : : Check solution in the statement "Jill's present age is three times her sister's age two years ago. " 18 = 3(8-2)
 Miscellaneous_Word_Problems/317123: The length of the Serumore Hotel's lobby exceeds its width by 4 feet. A rug covers the floor of the lobby except for a border 2 feet wide all around. If the area of this border of exposed floor is 68 square feet, what is the area of the rug?1 solutions Answer 227225 by ankor@dixie-net.com(15652)   on 2010-06-24 21:43:44 (Show Source): You can put this solution on YOUR website!The length of the Serumore Hotel's lobby exceeds its width by 4 feet. A rug covers the floor of the lobby except for a border 2 feet wide all around. If the area of this border of exposed floor is 68 square feet, what is the area of the rug? : Let x = the width of the rug then (x+4) = the length of the rug and x(x+4) = x^2 + 4x = the area of the rug : (x+4) = overall width (x+4) + 4 = (x+8) = overall length and (x+4)*(x+8) = x^2 + 12x + 32 =overall area : Overall area - rug area = 68 x^2 + 12x + 32 - (x^2 + 4x) = 68 x^2 + 12x + 32 - x^2 - 4x = 68 x^2 - x^2 + 12x - 4x = 68 - 32 8x = 36 x = x = 4.5 Find the area of the rug A = x(x+4) A = 4.5(4.5+4) A = 4.5(8.5) A = 38.25 sq/ft : : Check: Overall area = 4.5^2 + 12(4.5) + 32 = 106.25 106.25 - 38.25 = 68 confirms our solution
 Travel_Word_Problems/317173: The river is flowing from point A to B at a rate of 15 miles per hour. A boat moves on still water at 45 miles per hour. If it takes David 1 hour and 15 minutes to ride the boat on the river from A to B, how long does it take him to make the return trip from B to A?1 solutions Answer 227194 by ankor@dixie-net.com(15652)   on 2010-06-24 19:43:44 (Show Source): You can put this solution on YOUR website!The river is flowing from point A to B at a rate of 15 miles per hour. A boat moves on still water at 45 miles per hour. If it takes David 1 hour and 15 minutes to ride the boat on the river from A to B, how long does it take him to make the return trip from B to A? : Let t = time in hrs to go from B to A : change 1 hr 15 min to 1.25 hrs : Write a distance equation: dist = speed * time : A-B dist = B-A dist 1.25(45+15) = t(45-15) 1.25(60) = 30t 75 = 30t t = t = 2.5 hrs ; : Check solution by finding the distances 1.25(60) = 75 2.5(30) = 75