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In basketball, the number of points you score is given by
3x+2y+1z where
x is threepointers,
y is two-pointers, and
z is free throws (one-pointers). What is the total number of points scored by a player who makes 3 threepointers, 5 two-pointers, and 6 free throws?

In basketball, the number of points you score is given by $3 x+2 y+1 z$ where $x$ is threepointers, $y$ is two-pointers, and $z$ is free throws (one-pointers). What is the total number of points scored by a player who makes $3$ threepointers, $5$ two-pointers, and $6$ free throws?

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GCF and LCM: word problems

Full solution

Q. In basketball, the number of points you score is given by

3 x+2 y+1 z

where

x

is threepointers,

y

is two-pointers, and

z

is free throws (one-pointers). What is the total number of points scored by a player who makes

3

threepointers,

5

two-pointers, and

6

free throws?

Calculate three-pointers: Calculate the points from three-pointers. $\newline$ The player makes $3$ three-pointers, and each three-pointer is worth $3$ points. $\newline$ So, the points from three-pointers are $3 \times 3 = 9$ points.
Calculate two-pointers: Calculate the points from two-pointers. $\newline$ The player makes $5$ two-pointers, and each two-pointer is worth $2$ points. $\newline$ So, the points from two-pointers are $5 \times 2 = 10$ points.
Calculate free throws: Calculate the points from free throws. $\newline$ The player makes $6$ free throws, and each free throw is worth $1$ point. $\newline$ So, the points from free throws are $6 \times 1 = 6$ points.
Find total points: Add up all the points to find the total. $\newline$ Total points $= \text{points from three-pointers} + \text{points from two-pointers} + \text{points from free throws}$ $\newline$ Total points $= 9 + 10 + 6 = 25$ points.

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