In Miss Hoover's class, the ratio of boys to girls is $x$ to $y$. If the total number of children in the class is five times the number of boys in the class, and $x$ and $y$ are integers, which of the following could be the sum of $x$ and $y?$

Since the problem uses the word ratio, you can use the Ratio Box. However, the Ratio Box works best with numbers rather than variables. What to do? Plug In, of course! It's difficult to plug in for $x$ and $y$, because the ratio will depend on the number of boys in the class. Start with that number and say there are 4 boys in the class. The total number of students is therefore 20 , or five times 4 . Now, it's time to draw the Ratio Box and fill in what you know: Now use the box to find the ratio, which will give you your $x$ and $y$ values. If there are 4 boys, there are 16 girls. Plug in a simple multiplier, like 2 . Work backwards to find the parts of the ratio. If there are 4 actual boys and the multiplier is 2, the boys part of the ratio is 2. The girls part of the ratio is 8 . Here's what your filled-in box should look like: In this example, $x=2$ and $y=8$, so the sum is 10 , which happens to be one of the answer choices: (B). We got lucky with the numbers we picked and got exactly what we wanted. Sometimes, you may need to plug in a few times to see if there is a pattern. Regardless of where you start, the sum of the ratio parts in this class will always be a multiple of 5 .