How do I solve this type of Math problem on the ACT

Elkville High won a Friday Night basketball game by 10 points; the next night they record 25 points more than on Friday and again won by 10 points. The sum of the opponents’ scores for the 2 games was 109. How many points did Elkville score on Friday? The answers you can choose from are 37, 41, 46, 52, 72.

I feel like this is very easy to answer but I just don’t know how to approach these. These type of story problems where you pick the answer from the numbers they give you always stump me.

Well Dannie, the first thing you’re going to want to do on this type of problem is make 2 sets of equations.
First, it tells you that the sum of the opponents’ scores is 109, so that’s your first equation. F(Friday)+S(Saturday)=109. Then they tell you that Saturday’s game they scored 25 points more than Friday, so your next equation will be S=F+25.
The last thing you have to do is substitute S=F+25 into the first equation to solve for the opponents’ score on Friday. F+(F+25)=109.
Work that problem out and you’ll end up with F=42, but the problems asks for Elkville’s score, not the opponents’. Therefore, all you have to do is add 10 to 42 and that leaves you with 52.

Thanks Dylan, this was really helpful.

Or you can just guess and check the answers, starting with C. If it’s not C, then generally you can tell if you need a bigger answer or smaller answer.