Question

Louise, Tammy, Delores, and Sheryl score 78 points total in the tennis matches they play. They score a consecutive number of points from smallest to greatest in respect to the order of the names mentioned. How many points does Louise score?

Answer 1

`\huge\boxed{18\ \text{points}}`

We'll represent Louise's, Tammy's, Delores's, and Sheryl's point values with
`x`,
`x+1`,
`x+2`, and
`x+3` respectively since each one is 1 point more than the last.

Add all of these values up and set it all equal to
`78`.

`x+x+1+x+2+x+3=78`

Now, simplify.

`4x+6=78`

Subtract
`6` on both sides.

`\begin{aligned}4x+6-6&=78-6\\4x&=72\end{aligned}`

Divide both sides by
`4`.

`\begin{aligned}(4x)/(4)&=(72)/(4)\\x&=\boxed{18}\end{aligned}`

Since Louise's score is
`x`, the answer is
`18`.

Double-checking

To verify our answer, add the point totals
`18`,
`19`,
`20`, and
`21`.

This equals
`78`, so we can be sure the answer is correct.