Many situations can be represented by equations. Writing an equation to represent a situation can help us express how quantities in the situation are related to each other, and can help us reason about unknown quantities whose value we want to know. Here are two situations:

1. A camp counselor has a large bag that contains 34 cups of coconut. She uses 10 cups to make some trail mix. Then she uses the rest of the bag to make 144 identical granola bars. Campers want to know how much coconut is in each bar.

2. Kiran is trying to save $144 to buy a new guitar. He has $34 and is going to save $10 a week from money he earns mowing lawns. He wants to know how many weeks it will take him to have enough money to buy the guitar.

We see the same three numbers in the situations: 10, 34, and 144. How could we represent each situation with an equation?

In the camp situation, there is one part of 10 and then 144 equal parts of unknown size that all add together to 34. This can be represented by the equation $10+144x=34$. Since 24 is needed to get from 10 to 34, the value of $x$ is $(34−10) \div 144$ or $\frac16$. There is $\frac16$ cup of coconut in each serving.

In Kiran’s situation, there is one part of 34 and then an unknown number of equal parts of size 10 that all add together to 144. This can be represented by the equation $34+10x=144$. Since it takes 11 groups of 10 to get from 34 to 144, the value of $x$ in this situation is $(144-34)\div{10}$, or 11. It will take Kiran 11 weeks to raise the money for the guitar.