One store got 1.2 times as much apple cider as the second store. Every hour the first store was selling 90 liters of cider, while the second one was selling 80 liters per hour. In 2.5 hours the second store had 65 liters less than the first store. How many liters of cider were delivered to each store?
What I did: Let x = # of liters of cider the second store has
First Store: $1.2x$
Second Store: $x$
If every hour the first store was selling 90 liters of cider, while the second one was selling 80 liters per hour then I would get the equation:
$$1.2x-90(\text{unknown quantity})=(x-80(\text{unknown quantity}))$$
From the second part of the information my final equation would be : $$1.2x-90(2.5)=(x-80(2.5))+65$$ $$x=450$$
However, if I check the equation, something doesn't match up. Can someone tell me what I did wrong in making my equation?
Your answer looks correct, and we can check it:
One store got 1.2 times as much cider as another store. According to your answer, the second store got 450 liters of cider. Therefore the first one got 540 liters.
Each hour, the first store sold 90 liters while the second sold 80 liters. Here's what their inventory looks like:
$$\begin{array}{r|cc} & \text{first store} & \text{second store}\\\hline \text{0 hr} & 540 & 450 \\ \text{1 hr} & 450 & 370\\ \text{2 hr} & 360 & 290\\ \rightarrow\text{2.5 hr}& 315 & 250 \\ \end{array}$$
In 2.5 hours, the second store had 65 liters less than the first.
$$315 = 250 + 65 \quad\checkmark$$
If it helps, when I was solving this problem I acccidentally plugged in $x=450$ as the initial amount of cider in the first store rather than the second. Everything else checks out when you plug in the correct numbers, though!