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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.

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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



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