Noah is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Noah made a total of 11 shots altogether and scored a total of 29 points. Write a system of equations that could be used to determine the number of two point shots Noah made and the number of three point shots he made. Define the variables that you use to write the system.
Question
Noah is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Noah made a total of 11 shots altogether and scored a total of 29 points. Write a system of equations that could be used to determine the number of two point shots Noah made and the number of three point shots he made. Define the variables that you use to write the system.
Solution
Let's define:
x = number of two point shots Noah made y = number of three point shots Noah made
We know two things from the problem:
- Noah made a total of 11 shots. This can be written as: x + y = 11
- Noah scored a total of 29 points. Since each two point shot is worth 2 points and each three point shot is worth 3 points, this can be written as: 2x + 3y = 29
So, the system of equations that could be used to determine the number of two point shots (x) and three point shots (y) Noah made is:
x + y = 11 2x + 3y = 29
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