Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ Kylie and Fernando, the boy she was babysitting, were playing basketball together. Her score was $20$ points, and his score was $19$ points. Kylie wanted to make the game more fair, so she called a time-out and modified the rules a bit. Kylie explained that, for the rest of the game, she would get $3$ points per basket, and Fernando 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? $\newline$ Kylie and Fernando each made $\_$ baskets after the time-out, for a score of $\_$ .

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Solve a system of equations using any method: word problems

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

Kylie and Fernando, the boy she was babysitting, were playing basketball together. Her score was

20

points, and his score was

19

points. Kylie wanted to make the game more fair, so she called a time-out and modified the rules a bit. Kylie explained that, for the rest of the game, she would get

3

points per basket, and Fernando 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?

\newline

Kylie and Fernando each made

\_

baskets after the time-out, for a score of

\_

Set Up Equations: Let's denote the number of baskets Kylie and Fernando each made after the time-out as $b$ . Since they ended up with a tied score and they both made the same number of baskets, we can set up the following equation to represent their scores after the time-out: $\newline$ Kylie's score after time-out = $3 \text{ points/basket} \times b \text{ baskets}$ $\newline$ Fernando's score after time-out = $4 \text{ points/basket} \times b \text{ baskets}$
Calculate Total Scores: We know that before the time-out, Kylie's score was $20$ points and Fernando's score was $19$ points. We need to add the points they scored after the time-out to their initial scores to get the final tied score. The equations representing their total scores are: $\newline$ Kylie's total score = $20 + 3b$ $\newline$ Fernando's total score = $19 + 4b$ $\newline$ Since their final scores are tied, we can set these two expressions equal to each other: $\newline$ $20 + 3b = 19 + 4b$
Solve for b: To find the value of ＂b＂, we need to solve the equation from Step $2$ . We will subtract $3b$ from both sides and also subtract $19$ from both sides to isolate ＂b＂: $\newline$ $20 + 3b - 3b = 19 + 4b - 3b$ $\newline$ $20 - 19 = 4b - 3b$ $\newline$ $1 = b$
Determine Final Scores: Now that we have found that ＂b＂ equals $1$ , we can determine the number of baskets each person made after the time-out and their final scores. Since ＂b＂ is $1$ , we substitute ＂b＂ with $1$ in the equations for their total scores: $\newline$ Kylie's total score = $20 + 3(1) = 20 + 3 = 23$ $\newline$ Fernando's total score = $19 + 4(1) = 19 + 4 = 23$
Final Answer: We have found that Kylie and Fernando each made $1$ basket after the time-out, and their final scores were both $23$ points. This answers the question prompt.