Question

Eva and Brody, the boy she was babysitting, were playing basketball together. Her score was 18 points, and his score was 20 points. Eva wanted to make the game more fair, so she called a time-out and modified the rules a bit. Eva explained that, for the rest of the game, she would get 3 points per basket, and Brody would get 2 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 points did each person have at the end? How many baskets did each person make after the time out?

Answer 1

After the timeout, both Eva and Brody made 2 baskets each, leading to a tied final score of 24 points for both players.

Step-by-step explanation:

Initially, Eva's score was 18 points, and Brody's score was 20 points. After changing the rules, Eva received 3 points per basket, and Brody received 2 points per basket. To find out how many baskets each person made after the timeout and what their final scores were, we can set up an equation assuming they made x number of baskets each. For Eva, the new score will be 18 + 3x, and for Brody, the new score will be 20 + 2x. Since their scores are tied, we can equate these two expressions.

So, we have:

18 + 3x = 20 + 2x

Subtracting 2x from both sides, we get:

18 + x = 20

Subtracting 18 from both sides, we get:

x = 2

Both Eva and Brody made 2 baskets after the timeout. Eva's final score would be 18 + 3(2) = 24 points, and Brody's final score would be 20 + 2(2) = 24 points, confirming that their scores were tied at the end.