Bake Sale Profit Calculation
A math club is having a bake sale as a fundraiser to raise money for an upcoming trip. They sell $ 54 $ cookies at three for $ \$1 $ , and $20$ cupcakes at $ \$2 $ each, and $ 35 $ brownies at $ \$1 $ each. If it cost the math club $\$ 15 $ to bake these items, what was their profit?
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Solution
To find the profit, we want to find out how much the math club earned from selling the various baked goods and subtract the cost of producing those goods, $ \$15$ , from the number we get.
First let's calculate how much the math club earned from selling cookies. The cookies were sold at a price of three for $\$ 1 $, so the math club earned $ 54\div 3\cdot \$1 = 18\cdot\$ 1= \$18 $ from selling cookies.
Next, let's calculate how much the club earned from selling cupcakes. At a price of $\$ 2 $ each, the club earned $ 20\cdot \$2=\$ 40 $ from selling cupcakes.
Finally, let's calculate how much the club earned from selling brownies. At a price of $ \$1$ each, the club earned $35\cdot\$1=\$35$ from selling brownies.
Now let's add up these numbers to find out how much the club earned in total and subtract $\$ 15 $ from that number to find the club's profit. We obtain \begin{align*}
\$ 18+\$40+\$ 35-\$15&=\$ 18+\$40+\$ 35-\$15\\
&=\$ 18+\$40+\$ 35+(-\$15)\\
&=\$ 18+\$40+(\$ 35+(-\$15))\\
&=\$ 18+\$40+(\$ 20)\\
&=\boxed{78}.\end{align*}Notice how we used the definition of subtraction, $a-b=a+(-b)$ to $\$ 35-\$15$ as $\$ 35+(-\$15)$ and the associative property of addition to group the numbers together.
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