Question

A basketball player scored 634 points making 362 shots, including 3-point field goals, 2-point field goals, and 1-point free throws. She made 26 more 2-point field goals than free throws. Find the number of each type of goal she made.

Answer 1

To determine the number of each type of goal scored by the basketball player, we set up a system of equations using the information provided and solve for the variables representing 3-point field goals, 2-point field goals, and 1-point free throws.

Step-by-step explanation:

To solve the problem of determining the number of each type of goal scored by the basketball player, we need to set up a system of equations based on the given information. The player made 362 shots in total, including 3-point field goals, 2-point field goals, and 1-point free throws. We are told that the player scored 634 points and that she made 26 more 2-point field goals than free throws.

Let's define the variables as follows:

• x = number of 3-point field goals
• y = number of 2-point field goals
• z = number of 1-point free throws

The given information can be turned into the following equations:

1. 3x + 2y + z = 634 (total points)
2. x + y + z = 362 (total shots)
3. y = z + 26 (26 more 2-point field goals than free throws)

Subtracting the second equation from the first gives us:

• 2x + y = 272

We can substitute the expression for y from the third equation into this new equation to solve for x:

• 2x + (z + 26) = 272
• 2x = 246 - z
• x = (246 - z) / 2

Now that we have x in terms of z, we can substitute x and y into the second original equation (x + y + z = 362) to find z. After finding z, we can find x using the expression for x in terms of z and then y using the third equation. Solving this system will give us the exact number of each type of goal.