Question

Gabrielle is making punch for a party. Her guests drank 1/2 of the punch, and she mistakenly spilled 20 cups of punch. By the end of the party, she only had 10 cups of punch left. Write and solve an equation in order to determine the initial number of cups that she started off with.

Answer 1

Let be x the initial number of cups of punch. Then, we can write in algebraic language the word problem: x/2 because her guests drank 1/2 of punch.

And we can write the equation:

`x-(x)/(2)-20=10`

Because there was an initial amount of cups of punch, and then this amount decreased until there were 10 cups of punch left.

Now, we can write the equation for x:

`\begin{gathered} x-(x)/(20)-20=10 \\ \text{ Add 20 from both sides of the equation} \\ x-(x)/(2)-20+20=10+20 \\ x-(x)/(2)=30 \\ (2x)/(2)-(x)/(2)=30 \\ (2x-x)/(2)=30 \\ (x)/(2)=30 \\ \text{ Multiply by 2 from both sides} \\ (x)/(2)\cdot2=30\cdot2 \\ \boldsymbol{x=60} \end{gathered}`

Therefore, the initial number of cups that she started with was 60.