Show the algebraic equations that you use to solve the problems and include all necessary work?

Question

The perimeter of a swimming pool is 96m. The width is 3m more than half the length of the pool. Find the length and breadth of the pool.
96 = 2L + 2W

Answer 1

Solve the problem in terms of one or the other variables, then substitue that result back into the orignal.

You know the width is 3m more than half the length, so write that out as an axpression.

w=3+.5*L

Then put that value of w into your perimeter formula:

P=2L+2W = 2L+2(3+.5L)

Simplify that expression by distributing the 2:

P=2L+6+L = 3L+6

Then put in your value for the perimeter:

96=3L+6

Solve for L by subtracting 6 from both sides:

90=3L

Divibe by 3 to find L=30, then take that value and put it back into the original formula.

96=2L+2W = 2*30+2*W

Simplify and solve for W:

96=60+2W
36=2W
W=18.

So the length of the pool is 30m, and the width is 18m.

Answer 2

W = 1/2 L + 3 from "The width is 3m more than half the length of the pool."; substitute into your perimeter equation. Thus, 96 = 2L + 2(1/2 L + 3) = 2L + L + 6 = 3L + 6; so that 90 = 3L and L = 30.

Then W = 1/2 L + 3 = 15 + 3 = 18.

Check the answers using your perimeter equation.