maria plays 16 round of a game with her friend, she scored in 10 of them and the final score is 34 to 24. How many round did she score 5 points and how many rounds did she score 3

Question

her friends score doesn’t matter, and there must be 2 equations that can find out in how many rounds she scored 3 and in how many rounds she scored 5. the answer is two rounds 5 and eight rounds 3, but i need an equation to show for work.

Answer 1

Let x be the number of rounds in which she scored 3 and y the number in which she scored 5.

But she only scored in 10 of them so x+y=10.

Her total score was 34 so 3x+5y=34.

From the first equation y=10-x so we can substitute this in the other equation:

3x+5(10-x)=34, 3x+50-5x=34, 50-34=5x-3x, 16=2x, so x=8 and y=10-8=2.

So she scored 3 in 8 rounds and 5 in 2 rounds.

(There is enough information to find out the same for her friend, who scored 3 of each.)