# 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

 Dec 12, 2012 Cost of the Washer by: Staff AnswerPart IR = cost of refrigeratorW = cost of washerD = cost of dryerTogether, the cost of a refrigerator, washer, and dryer is \$1800.R + W + D = 1800The refrigerator costs \$250 more then the washerR = W + 250The dryer costs half as much as the washer.D = ½ * W Three equations, three unknownsUse substitution – solve for WR + W + D = 1800Since R = W + 250, substitute W + 250 for the variable R W + 250 + W + D = 1800Since D = ½ * W, substitute ½ * W for the variable DW + 250 + W + ½ * W = 1800Solve for the variable WCombine like termsW + 250 + W + ½ * W = 1800W + 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 = 1800Subtract 250 from each side of the equation (5W) / 2 + 250 - 250 = 1800 - 250(5W) / 2 + 0 = 1800 - 250(5W) / 2 = 1800 - 250(5W) / 2 = 1550Multiply each side of the equation by 22 * (5W) / 2 = 2 * 1550(5W) * (2 / 2) = 2 * 1550(5W) * (1) = 2 * 15505W = 2 * 15505W = 3100Divide each side of the equation by 5 5W / 5 = 3100 / 5W * (5 / 5) = 3100 / 5W * (1) = 3100 / 5W = 3100 / 5W = 620 -----------------------------------------------

 Dec 13, 2012 Cost of the Washer by: Staff ----------------------------------------------- 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 --------------------------------------------- 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