ALGEBRA II: EXTENDED SCHEDULING I_1_S1 1-6: Test Review

Question

a yard has a perimeter of 276 feet if six times the length of the yard equals seventeen times the width, what are its dimension's.

Answer 1

Starting with

(1) P = 2L + 2W = 276 and

(2) 6L = 17W

where P = perimeter, L = length, and W = width

We can solve the second equation for L by dividing both sides by 6. This gives

L = (17/6)W

Next we substitute (17/6)W for L in the first equation to give

P = 2(17/6)W + 2W = (17/3)W + 2W = (17/3 + 2)W = 276

17/3 + 2 = 17/3 + 6/3 = (17 +6)/3 = 23/3

So (17/3 + 2)W = (23/3)W = 276

Now we can solve for W if we multiply both sides by 3/23

(3/23)(23/3)W = W = (3/23)(276)

which gives us W = 36

L = (17/6)W = (17/6)(36) = (17)(6) = 102

Answer

The dimensions of the yard are

width = 36 feet

length = 102 feet