Question

If apples sell for \(\$\)0.68 per pound and Juanita bought 36 apples for \(\$\)8.16, then the average (arithmetic mean) number of apples per pound was

• A. \( \frac{1}{3} \)
• B. \( \frac{1}{2} \)
• C. 1
• D. 2
• E. 3

Hint:

Break down word problems into smaller, manageable steps. Here, the final goal is "apples per pound." Notice you have "total apples" but not "total pounds." Your first step must be to find the missing piece of information, "total pounds," using the cost data.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This is a multi-step problem involving rates. We need to find the average number of apples per pound. We are given the total number of apples and the total cost, as well as the cost per pound.
Step 2: Key Formula or Approach:
1. First, determine the total number of pounds of apples Juanita bought. We can find this by dividing the total cost by the cost per pound. \[ \text{Total Pounds} = \frac{\text{Total Cost}}{\text{Cost per Pound}} \] 2. Then, calculate the average number of apples per pound by dividing the total number of apples by the total number of pounds. \[ \text{Apples per Pound} = \frac{\text{Total Number of Apples}}{\text{Total Pounds}} \] Step 3: Detailed Explanation:
1. Find the total pounds bought: Total Cost = $8.16 Cost per Pound = $0.68 \[ \text{Total Pounds} = \frac{$8.16}{$0.68} \] To simplify this division, we can multiply the numerator and denominator by 100 to remove the decimals: \[ \text{Total Pounds} = \frac{816}{68} \] We can perform long division or simplify. Let's simplify by dividing both by 4: \(816 \div 4 = 204\). \(68 \div 4 = 17\). So, \( \frac{204}{17} \). Now, \(204 \div 17\). We know \(17 \times 10 = 170\). The remainder is \(204 - 170 = 34\). And \(17 \times 2 = 34\). So, \(17 \times 12 = 204\). Therefore, Juanita bought 12 pounds of apples. 2. Find the apples per pound: Total Number of Apples = 36 Total Pounds = 12 \[ \text{Apples per Pound} = \frac{36}{12} = 3 \] The average number of apples per pound was 3.
Step 4: Final Answer:
By first calculating the total weight of the apples (12 pounds) and then dividing the number of apples by this weight, we find the average is 3 apples per pound.