Question

Greta and Xavier, the boy she was babysitting, were playing basketball together. Her score was 32 points, and his score was 19 points. Greta wanted to make the game more fair, so she called a time-out and modified the rules a bit. Greta explained that, for the rest of the game, she would get 3 points per basket, and Xavier would get 4 points per basket. Then they played a bit longer. After the time-out, they both made the same number of baskets and ended up with a tied score. How many baskets did each person make after the time out? How many points did each person have at the end?

Answer 1

Let the number of baskets be x
Let the number of points be y

32 +3x = y
19 + 4x = y

Rearrange both equations then solve them as simultaneous equations
32 = y - 3x
19 = y - 4x

y - 3x = 32
- y - 4x = 19

x = 13

Substitute x into one of the equations
y - 3x = 32
y - (3 x 13) = 32
y - 39 = 32
y = 32 + 39
y = 71

Number of baskets (x) = 13
Number of points (y) = 71