https://file.aiquickdraw.com/mathbot/file/172706515396362yn179a.jpg

The problem discusses Gordon, a basketball player, who either makes two-point or three-point shots in each game. Here's a summary of the problem:

- Gordon has a 37.5% chance of scoring on each two-point shot and a 25% chance on each three-point shot.
- In one game, Gordon scored a total of 96 points.
- The ratio of successful two-point shots to successful three-point shots is 7:6.
- The goal is to determine how many successful three-point shots Gordon made in this game.

Let’s set up the solution:

### Step 1: Define Variables
- Let \( x \) be the number of successful two-point shots.
- Let \( y \) be the number of successful three-point shots.

From the problem, we know that:
- The total points scored by Gordon is \( 96 \). Therefore:
\[
2x + 3y = 96
\]
- The ratio of successful two-point shots to successful three-point shots is \( 7:6 \). Therefore:
\[
\frac{x}{y} = \frac{7}{6}
\]
or equivalently:
\[
x = \frac{7}{6}y
\]

### Step 2: Substitute and Solve
Substitute \( x = \frac{7}{6}y \) into the total points equation:
\[
2\left(\frac{7}{6}y\right) + 3y = 96
\]
This simplifies to:
\[
\frac{14}{6}y + 3y = 96
\]
\[
\frac{14}{6}y + \frac{18}{6}y = 96
\]
\[
\frac{32}{6}y = 96
\]
\[
\frac{16}{3}y = 96
\]
Multiplying both sides by 3:
\[
16y = 288
\]
Now, divide by 16:
\[
y = 18
\]

### Step 3: Conclusion
Gordon successfully made **18 three-point shots**.

Would you like more details or clarifications? Here are 5 related questions for further exploration:

1. How many successful two-point shots did Gordon make in the same game?
2. What percentage of Gordon's total points came from three-point shots?
3. How many total attempts did Gordon take if we know his shooting percentages?
4. What is the probability that Gordon would make 10 consecutive two-point shots?
5. How many points would Gordon have scored if he made the same number of attempts but at different success rates?

**Tip:** In basketball, understanding shooting ratios helps in analyzing a player's efficiency on the court!

Gordon adalah seorang pemain bola basket yang dalam setiap pertandingannya, hanya melakukan tembakan dua poin atau tembakan tiga poin. Peluang Gordon berhasil mendapatkan poin dari setiap tembakan dua poin adalah 37,5% dan dari setiap tembakan tiga poin adalah 25%. Dalam satu pertandingan, Gordon berhasil mencetak skor sebanyak 96 poin. Jika perbandingan banyak tembakan dua poin dan banyak tembakan tiga poin yang berhasil masuk ke keranjang adalah 7:6, maka banyak tembakan 3 poin yang berhasil masuk adalah ... tembakan.

Solve a basketball scoring problem involving Gordon's 96 points with two-point and three-point shots. The ratio of two-point to three-point shots is 7:6. Learn how to calculate the number of successful three-point shots Gordon made.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation