Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Celine and Malik, the boy she was babysitting, were playing basketball together. Her score was 20 points, and his score was 14 points. Celine wanted to make the game more fair, so she called a time-out and modified the rules a bit. Celine explained that, for the rest of the game, she would get 2 points per basket, and Malik 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? Celine and Malik each made _____ baskets after the time-out, for a score of _____.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Celine and Malik, the boy she was babysitting, were playing basketball together. Her score was 20 points, and his score was 14 points. Celine wanted to make the game more fair, so she called a time-out and modified the rules a bit.  Celine explained that, for the rest of the game, she would get 2 points per basket, and Malik 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?   Celine and Malik each made _____ baskets after the time-out, for a score of _____.

Bytelearn · Accepted Answer

Set Up Equation: Let's denote the number of baskets Celine and Malik made after the time-out as 'b'. Since they made the same number of baskets and ended up with a tied score, we can set up the following equation to represent the situation: Celine's total points = Malik's total points 20 + 2b = 14 + 4bIsolate 'b': To find the value of 'b', we need to solve the equation. Let's rearrange the terms to isolate 'b': 2b - 4b = 14 - 20 -2b = -6Solve for 'b': Now, divide both sides of the equation by -2 to solve for 'b': b = -6 / -2 b = 3Calculate Celine's Score: With 'b' found, we can calculate the final score for both Celine and Malik. Since they ended up with a tied score, we can use either Celine's or Malik's equation to find the final score: Celine's final score = 20 + 2b Celine's final score = 20 + 2(3) Celine's final score = 20 + 6 Celine's final score = 26Calculate Malik's Score: To confirm, we calculate Malik's final score using the same number of baskets: Malik's final score = 14 + 4b Malik's final score = 14 + 4(3) Malik's final score = 14 + 12 Malik's final score = 26

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