Question

How do you use proportions to solve how much money the restaurant made if it serves 250 people per day when they usually serve 100 people per day and takes in $908?

Answer 1

$2270.

We know that if 100 people are served, the restaurant takes in $908. Our question is: "If 100 people cause the restaurant to gain $908, what would the consequence of 250 people served be?". The proportion we have to write is thus
`100:908=250:x`
which must be read as "if 100 people cause $908, then 250 people must cause $`x`, and we need to find `x`.

Solving the generic proportion `a:b=c:d`, we know that `ad=bc`, and from this identity we can find the value we desire.

In our case, we know that `100x=908\cdot 250`, which yields
`x=\frac{908\cdot 250}{100}=\frac{227000}{100}=22700`.