Question

Scott needs to mail a CD to a friend he uses 43-cent stamps and 7-cent stamps to pay $1.78 in postage. How many of each stamp did Scott use

Answer 1

From the question, we have the following information available;

$\text{Total spent}=\text{ \ 1.78}$

Note that this is equivalent to 178 cents when reduced to its lowest form.

Also we are told that Scott purchased 43-cent and 7-cent stamps. That implies that he spent the exact amount to purchase stamps without change (no remainders).

178 is not a multiple of 43, which means he couldnt have bought all 43-cent stamps even if he wanted to.

172 is a multiple of 43 (that is, 43 times 4 = 172). However, if he bought 4 stamps for 172 cents then he would have just 6 cents as the remainder.

Hence, he could opt to buy 3 of the 43-cent stamps, and that would be;

$43\times3=129$

Therefore, if he spends 129 cents on stamps, he would have a remainder of 49 cents.

Note also that 49 is a multiple of 7. That means he can use the remainder to purchase 7-cent stamps as shown below;

$\begin{gathered} \text{Number of stamps}=\frac{49}{7} \\ \text{Number of stamps}=7 \end{gathered}$

This shows that he buys the stamps in the following order;

$\begin{gathered} 43-\text{cents}(3)=129 \\ 7-\text{cents}(7)=49 \\ \text{Total}=178 \end{gathered}$

ANSWER:

3 -- 43 cent stamps

7 -- 7-cent stamps