https://file.aiquickdraw.com/mathbot/file/1726185361472myxtr7g6.jpg

Let's solve the problem step by step.

The problem states that 96 mangoes are divided among \( X \), \( Y \), and \( Z \) in such a way that:
- \( X \) receives 4 times as many as \( Z \),
- \( Z \) receives 3 times as many as \( Y \),
- We are asked to find how many mangoes \( Y \) received.

### Step 1: Define Variables
Let the number of mangoes \( Y \) received be \( y \).

- Since \( Z \) receives 3 times as many as \( Y \), the number of mangoes \( Z \) received is \( 3y \).
- \( X \) receives 4 times as many as \( Z \), so \( X \) receives \( 4(3y) = 12y \).

### Step 2: Total Mangoes Equation
The total number of mangoes is 96. Therefore, the equation for the total distribution is:
\[
X + Y + Z = 96
\]
Substitute the expressions for \( X \) and \( Z \) in terms of \( y \):
\[
12y + y + 3y = 96
\]
\[
16y = 96
\]

### Step 3: Solve for \( y \)
Now, divide both sides by 16:
\[
y = \frac{96}{16} = 6
\]

### Step 4: Conclusion
So, \( Y \) received **6** mangoes.

The answer is (A) 6.

Would you like more details or further explanation?

Here are 5 related questions to explore:
1. If \( X \) received twice as many as \( Z \), and \( Z \) received 4 times as many as \( Y \), how many mangoes did \( Y \) receive?
2. How many mangoes did \( X \) and \( Z \) receive in the original problem?
3. What if the total number of mangoes was 120 instead of 96? How many would \( Y \) receive then?
4. If \( X \) received 5 times as many as \( Y \), and \( Z \) received the same amount as \( Y \), how would the mangoes be divided?
5. What if the number of mangoes was split equally among \( X \), \( Y \), and \( Z \)? How many would each receive?

**Tip:** Always start by defining the variables and relationships clearly before forming an equation when dealing with word problems.

Ninety-six mangoes are divided among X, Y, and Z in such a way that X received 4 times as many as Z and Z receives 3 times as many as Y. How much did Y receive?

Learn how to solve the mango distribution problem where 96 mangoes are divided among X, Y, and Z using algebraic substitution. This problem is ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation