Question

A store sells potatoes for 0.24 and tomatoes for 0.76. Fred bought 12 individual vegetables. If he paid $6.52 total, how many potatoes did Fred buy? 
 

• A. 5
• B. 8
• C. 7
• D. 2
• E.

Hint:

When working with decimals in equations, you can sometimes simplify the calculation by multiplying the entire equation by a power of 10 to eliminate the decimals. In this case, multiplying the cost equation by 100 would give \(24p + 76t = 652\), which might be easier to work with for some people.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem can be solved by setting up a system of two linear equations. One equation represents the total quantity of items, and the other represents the total cost.
Step 2: Key Formula or Approach:
Let \(p\) be the number of potatoes and \(t\) be the number of tomatoes. Equation 1 (Quantity): \(p + t = 12\) Equation 2 (Cost): \(0.24p + 0.76t = 6.52\) We need to solve this system for the variable \(p\).
Step 3: Detailed Explanation:
We will use the substitution method. From Equation 1, express \(t\) in terms of \(p\): \[ t = 12 - p \] Substitute this expression for \(t\) into Equation 2: \[ 0.24p + 0.76(12 - p) = 6.52 \] Distribute the 0.76: \[ 0.24p + 9.12 - 0.76p = 6.52 \] Combine the p-terms: \[ -0.52p + 9.12 = 6.52 \] Subtract 9.12 from both sides: \[ -0.52p = 6.52 - 9.12 \] \[ -0.52p = -2.60 \] Divide both sides by -0.52: \[ p = \frac{-2.60}{-0.52} = \frac{260}{52} \] To simplify the fraction, divide the numerator and denominator by 52: \[ p = 5 \] Step 4: Final Answer:
Fred bought 5 potatoes.