Question

The Moore family receive 27 pieces of mail on October 20 the mail consisted of letters ads bills in magazines how many letters did they receive if they receive the same number of letters as bills three more ads and bills and five more magazines then at

Answer 1

Let

b = number of bills received

a = number of ads received

l = number of letters received

m = number of magazines received

The Moore family received 27 pieces of mail, consisting of bills, ads, letters, and magazines:

b + a + l + m = 27

They received 3 more ads than letters:

a = l + 3

The same number of bills as letters:

b = l

5 more magazines than ads:

m = a + 5

Plug l = b into a = l + 3, we get: a = b + 3

Plug a = b + 3 into m = a + 5, we get: m = b + 3 + 5 that is m = b + 8

Now plug l = b, a = b + 3 and m = b + 8 into b + a + l + m = 27:

`\begin{gathered} b\text{ + b + b + 3 + b + 8 = 27} \\ 4b\text{ + 11 = 27} \end{gathered}`

collect like terms

`\begin{gathered} 4b\text{ = 27 - 11} \\ 4b\text{ = 16} \\ divide\text{ both side by 4} \\ b\text{ = }(16)/(4) \\ b\text{ = 4} \end{gathered}`

Hence the Moore family received 4 letters