# Balanced Models - Pool Word Problem

if the perimeter of a pool is 212m and the length is 12m longer than the width, what is the length and width.

### Comments for Balanced Models - Pool Word Problem

 Apr 19, 2012 Balanced Models - Pool Word Problem by: Staff Question: if the perimeter of a pool is 212m and the length is 12m longer than the width, what is the length and width. Answer: P = perimeter of pool L = length of pool W = width of pool The equation for the perimeter of the pool (a rectangle) is: P = 2L + 2W perimeter of a pool is 212 m P = 212 m 212 = 2L + 2W 2L + 2W = 212 length is 12m longer than the width L = W + 12 You now have two equations with two unknowns: 1st equation: 2L + 2W = 212 2nd equation: L = W + 12 Solve for W Substitute W + 12 for L in the 1st equation 2L + 2W = 212 2*(W + 12) + 2W = 212 Eliminate the parentheses using the distributive law 2*(W + 12) + 2W = 212 2*W + 2*12 + 2W = 212 Combine like terms 2W + 24 + 2W = 212 2W + 2W + 24 = 212 (2W + 2W) + 24 = 212 (4W) + 24 = 212 4W + 24 = 212 Subtract 24 from each side of the equation 4W + 24 - 24 = 212 – 24 4W + 0 = 212 - 24 4W = 212 - 24 4W = 188 Divide each side of the equation by 4 4W/4 = 188/4 W*(4/4) = 188/4 W*(1) = 188/4 W = 188/4 W = 47 Substitute 47 for L in the 2nd equation: L = W + 12 L = 47 + 12 L = 59 >>> the final answer is: L = 59 m W = 47 m Thanks for writing. Staff www.solving-math-problems.com