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 $4$.

$\begin{aligned}\frac{4x}{4}&=\frac{72}{4}\\x&=\boxed{18}\end{aligned}$

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.