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In basketball, the number of points you score is given by [tex]$3x + 2y + 1z[tex]$[/tex], where [tex]$[/tex]x[tex]$[/tex] is three-pointers, [tex]$[/tex]y[tex]$[/tex] is two-pointers, and [tex]$[/tex]z$[/tex] is free throws (one-pointers).

What is the total number of points scored by a player who makes 3 three-pointers, 5 two-pointers, and 6 free throws?



Answer :

GinnyAnswer
To determine the total number of points scored by a player who makes 3 three-pointers, 5 two-pointers, and 6 free throws, we follow these steps:

1. Identify the values and their corresponding point contributions:
- Each three-pointer is worth 3 points. The player made 3 three-pointers.
- Each two-pointer is worth 2 points. The player made 5 two-pointers.
- Each free throw (one-pointer) is worth 1 point. The player made 6 free throws.

2. Set up the expression for total points using the provided formula:
[tex]\[ \text{Total Points} = 3x + 2y + z \][/tex]
Where:
- \( x \) represents the number of three-pointers,
- \( y \) represents the number of two-pointers, and
- \( z \) represents the number of free throws.

3. Plug in the given values into the expression:
- \( x = 3 \)
- \( y = 5 \)
- \( z = 6 \)

Substitute these values into the formula:
[tex]\[ \text{Total Points} = 3(3) + 2(5) + 6 \][/tex]

4. Calculate each term separately:
- Three-point contributions: \( 3 \times 3 = 9 \)
- Two-point contributions: \( 2 \times 5 = 10 \)
- Free throw contributions: \( 1 \times 6 = 6 \)

5. Sum all the contributions to get the total points:
[tex]\[ \text{Total Points} = 9 + 10 + 6 \][/tex]

6. Add the values together to find the final result:
[tex]\[ \text{Total Points} = 25 \][/tex]

So, the total number of points scored by the player is [tex]\(\boxed{25}\)[/tex].

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