Problem 249

On Monday, Shane bought 4 boxes of cherries at a cost of $\$2.00\times4=\$8.00$.

He also bought 3 boxes of plums at a cost of $\$3.00\times3=\$9.00$, and 2 boxes of blueberries at a cost of $\$4.50\times2=\$9.00$.

In total, Shane paid $\$8.00+\$9.00+\$9.00=\$26.00$.
On Wednesday, Shane bought 2 boxes of plums at at cost of $\$3.00\times2=\$6.00$.

Since Shane spent $22.00 in total, he spent$\$22.00-\$6.00=\$16.00$ on boxes of cherries.

The price of each box of cherries is $2.00, and so Shane bought$$\$16.00\div\$2.00=8\$$ boxes of cherries.
Solution 1

On Saturday, Shane gave the cashier $100.00 and received$14.50 in change, and so Shane spent $\$100.00-\$14.50=\$85.50$.

Of the $85.50, Shane spent$$\$4.50\times3=\$13.50\$$ on 3 boxes of blueberries.

Therefore, Shane spent $\$85.50-\$13.50=\$72.00$ on boxes of plums and boxes of cherries.

If Shane bought $c$ boxes of cherries, then he bought twice as many boxes or $2c$ boxes of plums.

The cost of $c$ boxes of cherries is $\$2.00\times c=\$2c$.

The cost of $2c$ boxes of plums is $\$3.00\times2c=\$6c$.

Shane spent a total of $\$2c+\$6c=\$8c$ on boxes of plums and boxes of cherries, and so $8c=72$ or $c=9$.

Therefore, Shane bought 9 boxes of cherries.

Solution 2

As in Solution 1, we begin by determining that Shane spent $\$72.00$ on boxes of plums and boxes of cherries.

For every 1 box of cherries that Shane bought, he purchased 2 boxes of plums.

The cost of 1 box of cherries and 2 boxes of plums is $\$2.00+2\times\$3.00=\$8.00$ and $\$72.00\div\$8.00=9$, so Shane bought 9 boxes of cherries (and $2\times9=18$ boxes of plums).

Note: In both solutions, we may check that the cost of 9 boxes of cherries, 18 boxes of plums, and 3 boxes of blueberries is $9\times\$2.00+18\times\$3.00+3\times\$4.50=\$85.50$, and so the correct change from $100.00 is$14.50, as expected.