Question

Robert loves fruits. With his monthly allowance, he can buy either 50 apples or 40 bananas. One month, he decides to save 10% of his allowance. After buying 20 bananas, how many apples can he buy?
 

Hint:

When dealing with budget allocation problems, calculate the cost per unit and track remaining amounts systematically after each expense.

Answer 1

1. The cost of 50 apples is equal to Robert’s full allowance. Thus, the cost of one apple is: \[ \text{Cost of one apple} = \frac{\text{Allowance}}{50} \] Similarly, the cost of one banana is: \[ \text{Cost of one banana} = \frac{\text{Allowance}}{40} \] 2. Robert saves 10% of his allowance. Thus, the remaining amount he spends is: \[ \text{Remaining allowance} = 0.9 \times \text{Allowance} \] 3. After buying 20 bananas, the money spent on bananas is: \[ \text{Cost of 20 bananas} = 20 \times \frac{\text{Allowance}}{40} = \frac{\text{Allowance}}{2} \] 4. The remaining money is: \[ \text{Remaining money after bananas} = 0.9 \times \text{Allowance} - \frac{\text{Allowance}}{2} = 0.4 \times \text{Allowance} \] 5. The number of apples Robert can buy with the remaining money is: \[ \text{Number of apples} = \frac{0.4 \times \text{Allowance}}{\frac{\text{Allowance}}{50}} = 20 \] Conclusion: Robert can buy 20 apples with the remaining money.