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 To find the range of \( X \), we will solve the inequalities one at a time. 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 possible values for \( X \) are between 5 and 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 upper limit of 10) - C. \( 5 \leq X \leq 10 \) (Correct, as it includes the full range we calculated) - D. \( 8 \leq X \leq 10 \) (Incorrect, as it does not include values less than 8) ### Conclusion The correct answer is **C. \( 5 \leq X \leq 10 \)**, which accurately reflects the range of values for \( X \) based on the total cost constraints. ### Revision Summary - Tope bought \( X \) oranges and \( 2X \) mangoes, leading to a total cost of \( 13X \). - The total cost must be between N65.00 and N130.00, leading to the inequality \( 65 \leq 13X \leq 130 \). - Solving the inequalities gives the range \( 5 \leq X \leq 10 \). - The correct option is C, as it encompasses the entire range of possible values for \( X \).