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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Katie and Percy, the boy she was babysitting, were playing basketball together. Her score was points, and his score was points. Katie wanted to make the game more fair, so she called a time-out and modified the rules a bit. Katie explained that, for the rest of the game, she would get point per basket, and Percy would get 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?Katie and Percy each made baskets after the time-out, for a score of .
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Katie and Percy, the boy she was babysitting, were playing basketball together. Her score was points, and his score was points. Katie wanted to make the game more fair, so she called a time-out and modified the rules a bit. Katie explained that, for the rest of the game, she would get point per basket, and Percy would get 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?Katie and Percy each made baskets after the time-out, for a score of .
- Define variables: Let's define the variables.Let be the number of baskets Katie makes after the time-out.Let be the number of baskets Percy makes after the time-out.Since they made the same number of baskets, we have .
- Write equations: Write the equations based on the points each person gets per basket and their initial scores.Katie's score after the time-out will be her initial score plus point per basket she makes.Katie's score = Percy's score after the time-out will be his initial score plus points per basket he makes.Percy's score = Since their scores are tied, we can set these two expressions equal to each other.
- Substitute and simplify: Substitute with since .
- Solve for x: Solve for x.Subtract from both sides:Subtract from both sides:Divide both sides by :
- Calculate final scores: Since , Percy also made baskets after the time-out.
- Calculate final scores: Since , Percy also made baskets after the time-out.Calculate the final score for both Katie and Percy.Katie's final score = Percy's final score =
