Chapter 9, Problem 4MPS

To determine

To Find: What does the cantaloupe cost?

Answer to Problem 4MPS

  $\$0.77$

Explanation of Solution

Given: Eight ears of corn and cantaloupe cost $\$2.37$ . Six ears of corn and $3$ cantaloupe cost $\$3.51$

Let $a$ be the price of corn and $b$ be the price of cantaloupe

Then

According to the given

  $\begin{array}{l}8a+b=\mathrm{2.37....}(i)\\ 6a+3b=\mathrm{3.51...}(ii)\end{array}$

Solving the equations

Multiply the first equation by $-3$

  $\begin{array}{l}(-3)8a+b=2.37\\ -24a-3b=-\mathrm{7.11...}(iii)\end{array}$

Now

Add equation second and third

  $\begin{array}{l}6a+3b+-24a-3b=-7.11+3.51\\ -18a=-3.60\\ a=0.20\end{array}$

Substitute $a=0.20$ in equation first

  $\begin{array}{l}8(0.20)+b=2.37\\ b=0.77\end{array}$

Hence, the cost of cantaloupe is $\$0.77$