Lebron James scored 34 points on a combination of 21 foul shots (1 point) and two pointers. How many shots of each type did he make.
number of foul shots --- x
number of 2 ptrs ------- 21-x
solve for x:
x + 2(21-x) = 34
x=8 is number of foul shots
21-x = 21-8
= 13 is the number of two pointer shots.
To determine the number of shots Lebron James made, we'll use algebraic equations and solve for the variables.
Let's use the variables:
- x to represent the number of two-point shots made
- y to represent the number of foul shots made
According to the given information:
1. Each foul shot is worth 1 point.
2. Each two-point shot is worth 2 points.
3. Lebron James scored a total of 34 points.
Based on this, we can create two equations:
Equation 1: x + y = total shots
Equation 2: 2x + 1y = total points
Since we're trying to find the number of shots of each type (two-pointers and foul shots), we'll substitute the total shots with "21" in Equation 1 and the total points with "34" in Equation 2:
Equation 1: x + y = 21
Equation 2: 2x + 1y = 34
From Equation 1, we can solve for x:
x = 21 - y
Now we can substitute this value in Equation 2:
2(21 - y) + y = 34
Expanding and simplifying:
42 - 2y + y = 34
42 - y = 34
-y = 34 - 42
-y = -8
y = 8
Now substitute the value of y back into Equation 1 to find x:
x + 8 = 21
x = 21 - 8
x = 13
Therefore, Lebron James made 13 two-point shots and 8 foul shots to score a total of 34 points.