Solving equations

Question

the perimenter of a playing field is 348 yards. the length 6 yards less than quadriple the width

Answer 1

Assuming that this playing field is rectangular in shape and has the sides a & b, the perimeter is 2a + 2b.

If the perimeter is 348 yards we get: 348 = 2a +2b.

Using "a" for the length and "b" for the width, as well as the description that "the length [is] 6 yards less than the quardr[u]ple the width", we get a = 4b -6.

Now we substitute the "a" in the first equation with the "4b - 16" from the second, as they are equal.

We get 348 = 2(4b - 6) + 2b and can solve.

348 = 2(4b - 6) + 2b | distribute parenthesis

348 = 8b - 12 + 2b | combine like terms

348 = 10b - 12 | +12

360 = 10b | /10

36 = b

Using the second equation we get "a":

a = 4b - 6

a = 4*36 - 6

a = 144 - 6

a = 138

Verify:

348 = 2a +2b

348 = 2 * 138 + 2 * 36

348 = 276 + 72

348 = 348

Check!