I need help with this

Question

On January 14, the Jones family received 27 pieces of mail, consisting of magazines, bills, letters, and ads. If they received three more bills than letters, five more ads than bills, and the same number of magazines as letters, how many magazines did they receive?

Answer 1

Try this for starters:

Ads

Bills

Letters

Magazines

Let the variables A, B, L, M represent the number of each.

Then:

A + B + L + M = 27 I(pieces of mail received by Jones family)

B = L + 3 (bills is 3 more then letters)

A = B + 5 (ads is 5 more then bills)

M = L (magazines is same number as letters).

We want the number of magazines, but looks like most everything is in terms of L. If we solve for L first, then M will be the same value.

Try replacing all letters in the 1st equation with expressions in terms of L.

A + B + L + L = 27 (M=L)

A + (L + 3) + L + L = 27 (B = L+3)

(B + 5) + L + 3 + L + L = 27 (A = B+5)

((L + 3) +5) + L + 3 + L + L = 27 (B = L+3)

So what we have is:

L + 3 + 5 + L + 3 + L + L = 27

4L + 11 = 27.

Take if from there solving for L. And since M = L, that will be the answer to the question.

As a check determine the values of A and B too, add the results to make sure they combine to 27.

Answer 2

Let m, b, l and a be the mail received.

m + b + l +a = 27

b = l+3

a = b + 5

l = m

Substituting:

m + (m+3) + m +((m+3)+5)=27

4m +11 = 27

4m = 16

m = 4

They received 4 magazines.