Question

Sarah and Bryan went shopping and spent a total of $47.50. Bryan spent $15.50 less than what Sarah spent. How much did Bryan spend?

Answer 1

`$16.00`

Explanation:

Let the amount that Sarah spent be denoted by `s` and the amount that Bryan spent be denoted by `b`.

"Sarah and Bryan went shopping and spent a total of `$47.50`":

Eq1: `s + b = 47.50`

"Bryan spent `$15.50` less than what Sarah spent":

Eq2: `b = s - 15.50`

Now we need to solve for `b`. First we'll solve Eq1 to get an expression for `s`. Then we can substitute that result into Eq2 to find `b`, which is what we are searching for!

Solving Eq1 for `s`:
Eq3: `s = 47.50 - b`

Eq3 -> Eq2:
`b = (47.50-b)-15.50`
`b = 32.00 - b`
`2b = 32.00`
`=>color(green)(b = 16.00)`

Hence, Bryan spent `color(green)($16.00)`.