I have tried over and over again, I can’t figure this out!!

Question

On June 13, the Jones family received 31 pieces of mail, consisting of bills, letters, magazines, and ads. If they receive three more letters and magazines, five more ads and letters, and the same number of bills as magazines, how many bills did they receive

Answer 1

That makes more sense. Ok, let's break this down.

For purposes of this problem, I will use the first letter of each item as a variable. I.e. "b" for bill, "l" for letter, etc. We get the basic equation b+l+m+a = 31

The problem states:

"three more letters than magazines, five more ads than letters, and the same number of bills as magazines".

We indicate these as

l = m + 3

a = l +5

b = m

Since we're solving for bills, we'll keep things in terms of "b". We take our original equation: b+l+m+a = 31 and start substituting.

First b for m.

b + l + b + a = 31

Since l = m + 3 and b = m and we can say l = b + 3 b + b + 3 + b + a = 31

Now let’s work on the “a”. Since a = l + 5, and we already determined that l = b + 3 we can rewrite it as a = b + 3 + 5 or b + 8 b + b + 3 + b + b + 8 = 31.

Now simplify: 4b + 11 = 31. Subtract 11 on both sides 4b = 20. Divide by both sides by 4 to get "b" by itself and you get b = 5 or 5 bills.

You can check your work by plugging in the numbers:

b = 5

b+l+m+a = 31

l = m + 3

a = l + 5

b = m

We plug in 5 for b and m

5 + l + 5 + a; now solve l = m + 3 and plug into the equation

5 + (5 + 3) + 5 + a; now solve for a = l + 5 5 + (5 + 3) + 5 + (5 + 3 + 5) 5 + 8 + 5 + 13 = 31 - It works!

three more letters than magazines? l = 8, m = 5 --- check!

five more ads than letters? l = 8, a = 13 --- check!

and the same number of bills as magazines? 5 and 5 --- check!

I hope this all made sense and helps (felt like a while to type out!). If you have any questions on this or would like to consider me as a tutor, please don't hesitate to reach out - I can do video conference sessions! Good luck, Jessica!