Question

Two oranges, three bananas and four apples cost Rs.15. Three oranges, two bananas and one apple cost Rs.10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?

• A. Rs.10
• B. Rs.8
• C. Rs.15
• D. cannot be determined

Hint:

When asked for the total cost, reduce the system to eliminate variables and focus only on the required combination.

Answer 1

The Correct Option is C

Let the cost of one orange be \( x \), one banana be \( y \), and one apple be \( z \).
From the first equation: \[ 2x + 3y + 4z = 15 \tag{1} \] From the second equation: \[ 3x + 2y + z = 10 \tag{2} \] We want to calculate the cost of: \[ 3x + 3y + 3z 3(x + y + z) \] Let’s try to find \( x + y + z \) from (1) and (2).
Multiply (2) by 4: \[ 12x + 8y + 4z = 40 \tag{3} \] Now subtract (1) × 1: \[ (12x + 8y + 4z) - (2x + 3y + 4z) = 40 - 15
(10x + 5y) = 25 2x + y = 5 \tag{4} \] Now go back to equation (2): \[ 3x + 2y + z = 10 \text{Let’s isolate } z \text{ using (4).} \] From (4), \( y = 5 - 2x \), plug into (2): \[ 3x + 2(5 - 2x) + z = 10 3x + 10 - 4x + z = 10 -x + z = 0 z = x \tag{5} \] Now we know: From (4): \( y = 5 - 2x \) From (5): \( z = x \) Now evaluate: \[ 3x + 3y + 3z = 3(x + y + z) \] Substitute: \[ = 3(x + (5 - 2x) + x) = 3(x + 5 - 2x + x) = 3(5) = \boxed{15} \]