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**Answers to Station #1 Word Problems**

One number is 36 less than another. Together both numbers total 90. What is each number? 1st Number = x 2nd Number = x – 36 Equation is…..x + x – 36 = 90 x + x – 36 = 90 2x – 36 = 90 2x = 126 x = 63 The 1st number is 63 and the 2nd number is 27. Timmy has $52 more than Johnny. Together they have $160. How much does each have? Johnny = J Timmy = J + 52 Equation is…..J + J + 52 = 160 J + J + 52 = 160 2J + 52 = 160 2J = 108 J = 54 Johnny has $54.00 and Timmy has $

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**Answers to Station #2 Word Problems**

The sum of two numbers is 82. The larger number is one more than twice the smaller number. Find the numbers. Smaller number = s Larger number = 2s + 1 Equation…..s + 2s + 1 = 41 s + 2s + 1 = 41 3s + 1 = 41 3s = 40 s = 13.3 The smaller number is 13.3 and the larger number is 27.6. Ida Claire is six times as old as Claire Fie. The sum of their ages is 77 years. Find the age of each. Claire Fie = f Ida Claire = 6f Equation…..f + 6f = 77 f + 6f = 77 7f = 77 f = 11 Ida Claire is 11 years old and Ida Claire is 66 years old.

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**Answers to Station #3 Word Problems**

The length of a rectangle is equal to three the width. The perimeter of the rectangle is 156 inches. What is the width of the rectangle? width = w length = 3w Equation…..w + 3w = 156 w + 3w = 156 4w = 156 w = 39 The width of the rectangle is 39 inches and the length is 117 inches. The sum of two consecutive numbers is What are the numbers? 1st number = x 2nd number = x + 1 Equation…..x + x + 1 = 415 x + x + 1 = 415 2x + 1 = 415 - 1 = - 1 2x = 414 x = 207 The 1st number is 207 and the 2nd number is 208.

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**Answers to Station #4 Word Problems**

The sum of three consecutive numbers is Find the numbers. 1st number = n 2nd number = n + 1 3rd number = n + 2 Equation…..n + n n + 2 = 315 n + n n + 2 = 315 3n + 3 = 315 -3 = -3 3n = 312 n = 104 The 1st number is 104, the 2nd number is 105, and the 3rd number is 106. The sum of four consecutive numbers is What are the numbers? 1st number = x 2nd number = x + 1 3rd number = x + 2 4th number = x + 3 Equation…..x + x x x + 3 = 230 x + x x x + 3 = 230 4x + 6 = 230 -6 = -6 4x = 224 x = 56 The 1st number is 56, the 2nd number is 57, the 3rd number is 58, and the 4th number is 59.

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**Answers to Station #5 Word Problems**

An equal number of nickels, dimes, and quarters has a value of $ How many of each coin are there. x = number of each coin .05x + .10x + .25x = $4.40 .40x = $4.40 x = 11 There are a total of 11 nickels, 11 dimes, and 11 quarters. 11 x .05 = 0.55 11 x .10 = 1.10 11 x .25 = 2.75 $4.40 A collection of 16 coins is valued at $.58. There are four more nickels than dimes and six more pennies than dimes. How many of each coin are there? dimes = d nickels = d + 4 pennies = d + 6 Equation = d + d d + 6 = 16 d + d d = 16 3d + 10 = 14 - 10 = - 10 3d = 6 d = 2 There are 2 dimes, 6 nickels and 8 pennies.

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**Answers to Station #6 Word Problems**

A rectangle has a length that is 8 meters less than 6 times the width. The perimeter is 460 meters. What is the length and width? width = w length = 6w – 8 Equation…..2w + 2(6w – 8) = 460 2w + 2(6w – 8) = 460 2w + 12w – 16 = 460 14w – 16 = 460 + 16 = + 16 14w = 476 w = 34 The width of the rectangle is 34 meters and the length of the rectangle is 196 meters. A landowner wants to fence a triangular parcel of land. One side is twice the second; the third side is 40 meters less than 3 times the second side. The perimeter of the parcel is 320 meters. What is the length of each side? 1st side = s 2nd side = 2s 3rd side = 3(2s) – 40 Equation…..s +2s +3(2s) – 40 = 320 s + 2s + 3(2s) – = 320 s + 2s + 6s – = 320 9s – = 320 = +40 9s = 360 s = 40 The 1st side is 40m, the 2nd side is 80m and the 3rd side is 200m.

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**Answers to Bean Salad #1 and #2**

Three Bean Salad #1 contains the same number of red beans as lima beans and three more black-eyed peas than red beans. There are a total of 18 beans. What is the number of each type of bean? red beans = r lima beans = r black-eyed peas = r + 3 r + r + r + 3 = 18 3r + 3 = 18 -3 = -3 3r = 15 r = 5 There are 5 red beans, 5 lima beans, and 8 black-eyed peas. Three Bean Salad #2 contains three times as many red beans as black-eyed peas and one more lima bean than red beans. There are eight beans in all. What is the number of each type of bean? black-eyed peas = b red beans = 3b lima bean = 3b + 1 b + 3b + 3b + 1 = 8 7b + 1 = 8 -1 = -1 7b = 7 b = 1 There are 3 red beans, 4 lima beans, and 1 black-eyed pea.

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**Answers to Station #7 Word Problems**

Three Bean Salad #2 contains….. Three times as many red beans as black-eyed peas; and One more lima bean than red beans. There are eight beans in all. What is the number of each type of bean? What is there were 50 beans in this mixture? red beans = 3b lima beans = 3b + 1 black-eyed peas = b 3b + 3b b = 8 7b + 1 = 8 - 1 = - 1 7b = 7 b = 1 There are 3 red beans, 4 lima beans, and 1 black-eyed peas. 3b + 3b b = 50 7b + 1 = 50 -1 = -1 7b = 49 b = 7 There are 21 red beans, 22 lima beans, and 7 black-eyed pea.

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