Question

Write a system of equations to describe the situation below, solve using substitution, and use the drop down menus to fill in the blanks.

Janet and Harold, the boy she was babysitting, were playing basketball together. Her score was 19 points, and his score was 20 points. Janet wanted to make the game more fair, so she called a time-out and modified the rules a bit. Janet explained that, for the rest of the game, she would get 2 points per basket, and Harold would get 1 point 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?

Janet and Harold each made
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baskets after the time-out, for a score of
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.

Answer 1

Let x = number of baskets each made after the time-out.
Janet's total: 19 + 2x
Harold's total: 20 + x
They tie, so 19 + 2x = 20 + x.

Solve by substitution:
19 + 2x = 20 + x
2x - x = 20 - 19
x = 1

Each made 1 basket after the time-out, and each ended with 19 + 2(1) = 21 (Janet) and 20 + 1 = 21 (Harold).

So: "each made 1 baskets after the time-out, for a score of 21."