Question

William is throwing a party for his math class and decides to visit Jones' Pi Bakery. There, cupcakes cost $$2$ and pies cost $$7.5$. William bought a total of $20$ items. In all, he spent $$73$. How many cupcakes and pies did he purchase?

• A. $6,14$
• B. $8,12$
• C. $12,8$
• D. $14,6$

Answer 1

The correct option is D $14,6$

Let $x=$ Number of cupcakes
$y=$ Number of pies
Step 1: Total items $=20$
So,
$x+y=20\dots \left(1\right)$

Step 2: Total money spent $=$ $$73$
So,
$2x+7.50y=73\dots \left(2\right)$
Step 3: Multiply equation $\left(1\right)$ by $2$
$2x+2y=40\dots \left(3\right)$

Step 4: Substract eqution $\left(3\right)$ from equation $\left(2\right)$


We get,
$5.5y=33$
$y=\frac{33}{5.5}$
$=\frac{33\times 10}{5.5\times 10}$
$=\frac{330}{55}$
$\Rightarrow y=6$
Plug $y=6$ into equation $\left(1\right)$ to get $x$
$x+6=20$
$x=20-6$
$\Rightarrow x=14$