John has $42. He purchased fifty mangos and thirty oranges with the whole amount. He then chose to return six mangoes for nine oranges as both quantities are equally priced. What is the price of each Mango?

Options

A. `0.4`
B. `0.45`
C. `0.5`
D. `0.6`

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information provided.

### Step 1: Define Variables
Let:
- \( X \) = price of one mango (in dollars)
- \( Y \) = price of one orange (in dollars)

### Step 2: Set Up the First Equation
John purchased 50 mangoes and 30 oranges for a total of $42. Therefore, we can write the equation:
\[ 50X + 30Y = 42 \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
John returned 6 mangoes for 9 oranges, and the cost of these quantities is equal. Thus, we can write the equation:
\[ 6X = 9Y \quad \text{(Equation 2)} \]
From this, we can express \( Y \) in terms of \( X \):
\[ Y = \frac{6}{9}X = \frac{2}{3}X \]

### Step 4: Substitute \( Y \) in Equation 1
Now, substitute \( Y \) in Equation 1:
\[ 50X + 30\left(\frac{2}{3}X\right) = 42 \]

### Step 5: Simplify the Equation
Calculating \( 30 \times \frac{2}{3}X \):
\[ 30 \times \frac{2}{3}X = 20X \]
So, the equation becomes:
\[ 50X + 20X = 42 \]
Combine like terms:
\[ 70X = 42 \]

### Step 6: Solve for \( X \)
Now, divide both sides by 70:
\[ X = \frac{42}{70} = \frac{6}{10} = 0.6 \]

### Conclusion
The price of each mango is \( \boxed{0.6} \) dollars.

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