To solve the problem, we need to analyze the information given about Tope's purchases of oranges and mangoes. Let's break it down step-by-step. ### Step 1: Define the Variables - Let \( X \) be the number of oranges Tope bought. - The cost of each orange is N5.00, so the total cost for oranges is \( 5X \). - Tope bought twice as many mangoes as oranges, which means she bought \( 2X \) mangoes. - The cost of each mango is N4.00, so the total cost for mangoes is \( 4(2X) = 8X \). ### Step 2: Set Up the Total Cost Equation The total cost for both oranges and mangoes can be expressed as: \[ \text{Total Cost} = \text{Cost of Oranges} + \text{Cost of Mangoes} = 5X + 8X = 13X \] ### Step 3: Establish the Range for Total Cost According to the problem, Tope spent at least N65.00 and at most N130.00. Therefore, we can set up the following inequality: \[ 65 \leq 13X \leq 130 \] ### Step 4: Solve the Inequalities Now, we will solve the inequalities for \( X \). 1. **Lower Bound:** \[ 65 \leq 13X \] Dividing both sides by 13: \[ X \geq \frac{65}{13} = 5 \] 2. **Upper Bound:** \[ 13X \leq 130 \] Dividing both sides by 13: \[ X \leq \frac{130}{13} = 10 \] ### Step 5: Combine the Results From the calculations above, we find: \[ 5 \leq X \leq 10 \] This means that the range of values for \( X \) is from 5 to 10, inclusive. ### Step 6: Identify the Correct Option Looking at the options provided: - A. \( 4 \leq X \leq 5 \) (Incorrect, as \( X \) must be at least 5) - B. \( 5 \leq X \leq 8 \) (Partially correct, but does not include the full range up to 10) - C. \( 5 \leq X \leq 10 \) (Correct, as it matches our derived range) - D. \( 8 \leq X \leq 10 \) (Incorrect, as it does not include values below 8) Thus, the correct answer is **C. \( 5 \leq X \leq 10 \)**. ### Summary of Key Points - Tope's total expenditure is calculated based on the number of oranges and mangoes. - The inequalities derived from the total cost give the range for \( X \). - The correct range of values for \( X \) is from 5 to 10. - The other options either do not cover the full range or are incorrect based on the calculations. ### Revision Summary - Define variables clearly for the problem. - Set up equations based on the information given. - Solve inequalities carefully to find the range of values. - Verify the answer against the provided options to ensure correctness.