Question

The Moore family received 35 pieces of mail on February 2. The mail consisted of letters, magazines, bills, and ads, How many letters did they receive if they receivedthree more magazines than bills, five more ads than magazines, and the same number of letters as bills?

Answer 1

Let:

• l, be the number of letters recieved

,

• m, be the number of magazines recieved

,

• b, be the number of bills recieved

,

• a, be the number of adds recieved

Since we know that the Moore family received 35 pieces of mail in total, we'll have that:

$l+m+b+a=35$

We'll call this equation equation 1.

Now, we know that they received three more magazines than bills. This way,

$m=b+3$

We'll call this equation equation 2.

We also know that they recieved five more ads than magazines. This way,

$a=m+5$

We'll call this equation equation 3.

For our last eqaution, we know that they recieved the same number of letters as bills. This way,

$l=b$

We'll call this equation equation 4.

First, we'll substitute equation 4 into equation 1:

$\begin{gathered} l+m+b+a=35\rightarrow b+m+b+a=35 \\ \Rightarrow m+a+2b=35 \end{gathered}$

Now, we'll substitute equation 3:

$\begin{gathered} m+a+2b=35\rightarrow m+m+5+2b=35 \\ \rightarrow2m+2b=30 \\ \Rightarrow m+b=15 \end{gathered}$

Lastly, we substitute equation 2:

$\begin{gathered} m+b=15\rightarrow b+3+b=15 \\ \rightarrow2b+3=15\rightarrow2b=12\rightarrow b=\frac{12}{6} \\ \\ \Rightarrow b=2 \end{gathered}$

From equation 4, we'll have that:

$l=b\rightarrow l=2$

This way, we can conclude that they recieved 2 letters.