Audrey and Gabriel, the boy she was babysitting, were playing basketball together. Her score was 30 points, and his score was 10 points. Audrey wanted to make the game more fair, so she called a time-out and modified the rules a bit. Audrey explained that, for the rest of the game, she would get 3 points per basket, and Gabriel would get 7 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? Write a system of equations, graph them, and type the solution. ____ baskets

Question

Audrey and Gabriel, the boy she was babysitting, were playing basketball together. Her score was 30 points, and his score was 10 points. Audrey wanted to make the game more fair, so she called a time-out and modified the rules a bit.  Audrey explained that, for the rest of the game, she would get 3 points per basket, and Gabriel would get 7 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?  Write a system of equations, graph them, and type the solution.  ____ baskets

Bytelearn · Accepted Answer

Define variables:  Let's define the variables: Let $ a $ be the number of baskets Audrey makes after the time-out, and $ g $ be the number of baskets Gabriel makes after the time-out. Since they made the same number of baskets, $ a = g $. Equation for scores:  Audrey's score increases by 3 points for each basket she makes, and Gabriel's score increases by 7 points for each basket he makes. We know they ended up with the same score. So, the equation for their scores after the time-out is $ 30 + 3a = 10 + 7g $. Substitute and simplify:  Since $ a = g $, substitute $ g $ for $ a $ in the score equation: $ 30 + 3g = 10 + 7g $. Solve for g:  Solve for $ g $: Subtract 3g from both sides to get $ 30 = 10 + 4g $. Then subtract 10 from both sides to get $ 20 = 4g $. Finally, divide both sides by 4 to find $ g = 5 $. Find Audrey's baskets:  Since $ a = g $, Audrey also made 5 baskets after the time-out.

Full solution

More problems from Write and solve equations for proportional relationships

Related topics