Problema Solution
A basketball player scored 29 points in a game. The number of three-point field goals the player made was 21 less than three times the number of free throws (each worth 1 point). Twice the number of two-point field goals the player made was 9 more than the number of three-point field goals made. Find the number of free-throws, two-point field goals, and three-point field goals that the player made in the game.
Answer provided by our tutors
let
x = the number of free-throws scored
y = the number of two-point field goals scored
z = the number of three-point field goals scored
a basketball player scored 29 points in a game
x + 2y + 3z = 29
the number of three-point field goals the player made was 21 less than three times the number of free throws
z = 3x - 21
twice the number of two-point field goals the player made was 9 more than the number of three-point field goals made
2y = 9 + z
by solving the system of equations
x + 2y + 3z = 29
z = 3x - 21
2y = 9 + z
we find
x = 8 free-throws
y = 6 two-point field goals
z = 3 three-point field goals
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the basketball player scored 8 free-throws, 6 two-point field goals and 3 three-point field goals.