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Help - Word Problem – Solve for unknown cost











































Word Problem – Solve for the cost of the washer

Together, the cost of a refrigerator, washer, and dryer is $1800.

The refrigerator costs $250 more then the washer

The dryer costs half as much as the washer.

How much does the washer cost?

Comments for Help - Word Problem – Solve for unknown cost

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Dec 12, 2012
Cost of the Washer
by: Staff


Answer


Part I


R = cost of refrigerator

W = cost of washer

D = cost of dryer


Together, the cost of a refrigerator, washer, and dryer is $1800.

R + W + D = 1800


The refrigerator costs $250 more then the washer

R = W + 250


The dryer costs half as much as the washer.

D = ½ * W


Math – solve by substitution






Three equations, three unknowns

Use substitution – solve for W

R + W + D = 1800

Since R = W + 250, substitute W + 250 for the variable R

W + 250 + W + D = 1800


Since D = ½ * W, substitute ½ * W for the variable D

W + 250 + W + ½ * W = 1800


Solve for the variable W


Combine like terms

W + 250 + W + ½ * W = 1800

W + W + ½ * W + 250 = 1800

(W + W + ½ * W) + 250 = 1800

(2W/2 + 2W/2 + ½ * W) + 250 = 1800

(2W + 2W + W) / 2 + 250 = 1800

(5W) / 2 + 250 = 1800


Subtract 250 from each side of the equation

(5W) / 2 + 250 - 250 = 1800 - 250

(5W) / 2 + 0 = 1800 - 250

(5W) / 2 = 1800 - 250

(5W) / 2 = 1550


Multiply each side of the equation by 2

2 * (5W) / 2 = 2 * 1550

(5W) * (2 / 2) = 2 * 1550

(5W) * (1) = 2 * 1550

5W = 2 * 1550

5W = 3100


Divide each side of the equation by 5

5W / 5 = 3100 / 5

W * (5 / 5) = 3100 / 5

W * (1) = 3100 / 5

W = 3100 / 5

W = 620


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Dec 13, 2012
Cost of the Washer
by: Staff

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Part II

Since you now know that W = 620, solve for R by substituting 620 for W in the following equation:

R = W + 250

R = 620 + 250

R = 870


Solve for D by substituting 620 for W in the following equation:

D = ½ * W

D = ½ * 620

D = 310



Final Answer:


R = cost of refrigerator = $870

W = cost of washer = $620

D = cost of dryer = $310



Math – solved by substitution






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Check you answer. Substitute the numerical values for the variables in the following equation.

R + W + D = 1800

870 + 620 + 310 = 1800

1800 = 1800, OK → R = 870, W = 620, and D = 310 are valid solutions.





Thanks for writing.

Staff
www.solving-math-problems.com



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