Divide 1,380 among A, B and C, so that A gets 5 times of C and 3 times of B.

Options

A. `A=980, B=300, C=100 `
B. `A=880, B=200, C=300 `
C. `A=900, B=300, C=180 `
D. `A=800, B=300, C=280 `

Answer

To solve the problem of dividing 1,380 among A, B, and C such that A gets 5 times what C gets and 3 times what B gets, we can follow these steps:

### Step 1: Define the Variables
Let:
- \( C = x \) (the amount C receives)
- \( A = 5x \) (since A gets 5 times what C gets)
- \( B = \frac{5x}{3} \) (since A also gets 3 times what B gets, we can express B in terms of x)

### Step 2: Set Up the Equation
According to the problem, the total amount distributed among A, B, and C is 1,380. Therefore, we can write the equation:
\[ A + B + C = 1380 \]
Substituting the expressions for A, B, and C, we get:
\[ 5x + \frac{5x}{3} + x = 1380 \]

### Step 3: Clear the Fractions
To eliminate the fraction, we can multiply the entire equation by 3 (the denominator of the fraction):
\[ 3(5x) + 3\left(\frac{5x}{3}\right) + 3(x) = 3(1380) \]
This simplifies to:
\[ 15x + 5x + 3x = 4140 \]

### Step 4: Combine Like Terms
Now, combine the terms on the left side:
\[ 23x = 4140 \]

### Step 5: Solve for x
To find x, divide both sides by 23:
\[ x = \frac{4140}{23} = 180 \]

### Step 6: Calculate A, B, and C
Now that we have \( x \), we can find the amounts for A, B, and C:
- \( C = x = 180 \)
- \( A = 5x = 5 \times 180 = 900 \)
- \( B = \frac{5x}{3} = \frac{5 \times 180}{3} = 300 \)

### Step 7: Verify the Total
Finally, let's verify that the total adds up to 1,380:
\[ A + B + C = 900 + 300 + 180 = 1380 \]

### Conclusion
Thus, the amounts received by A, B, and C are:
- A = 900
- B = 300
- C = 180