Basketball player scored 12 times during one game. He scored a total of 18 points, two for each two-point Shot and one for each free throw. How many two-point shots did he make? How many free throws?
t + f = 12
2t + f = 18
6 and 6
To determine how many two-point shots the basketball player made, divide the total points by 2 since each two-point shot is worth 2 points:
18 points รท 2 = 9 two-point shots
Therefore, the basketball player made 9 two-point shots.
To determine how many free throws the basketball player made, subtract the number of two-point shots from the total number of shots:
12 shots - 9 two-point shots = 3 free throws
Therefore, the basketball player made 3 free throws.
To determine the number of two-point shots the basketball player made, we can first assume "x" to represent the number of two-point shots made. Since each two-point shot earns the player 2 points, the total number of points earned from two-point shots would be 2*x.
Similarly, the player scored one point for each free throw made. Let's assume "y" to represent the number of free throws made. So, the total points earned from free throws would be 1*y.
Given that the basketball player scored 18 points in total, we can set up the equation:
2*x + 1*y = 18
Now, we know that the player scored 12 times during the game. Since each two-point shot and each free throw counts as one score, the equation can be written as:
x + y = 12
To solve these equations simultaneously, we can use substitution or elimination method. Let's use the substitution method:
From the second equation, we can rewrite it as y = 12 - x. Now, substitute this expression for "y" in the first equation:
2*x + 1*(12 - x) = 18
Simplifying the equation:
2*x + 12 - x = 18
x + 12 = 18
x = 18 - 12
x = 6
Therefore, the basketball player made 6 two-point shots.
Now, substituting the value of "x" back into the second equation:
6 + y = 12
y = 12 - 6
y = 6
Hence, the basketball player made 6 free throws.
To summarize, the player made 6 two-point shots and 6 free throws during the game.