Chapter 9, Problem 7CT

To determine

To Find: Number of post cards did he buy of each size.

Answer to Problem 7CT

  $3$ small cards and $4$ large post cards.

Explanation of Solution

Given: John bought a total of $7$ post cards for $\$1.80$ .If the small post card cost $20\not\subset$ each and the large post card $30\not\subset$ each.

Let $s$ be the small post cards

And $l$ be the large post cards

Then

Total post cards

  $\begin{array}{l}l+s=7\\ s=7-l\mathrm{...}(i)\end{array}$

Cost of one small post cards = $\$0.20$

Cost of one large post card = $\$0.30$

Total amount he spend = $\$1.80$

Thus

Equation becomes

  $\begin{array}{l}\$0.20s+\$0.30l=\$1.80\\ 2s+3l=18\\ u\mathrm{sing}(i)\\ s=7-l\\ 2(7-l)+3l=18\\ 14-2l+3l=18\\ l=4\\ thus\\ s=7-l\\ s=7-4\\ s=3\end{array}$

Hence, $3$ small cards and $4$ large post cards.