Math Problem Statement

Apples cost $0.60 each and pears cost $0.80 each. If a total of 130 apples and pears cost $88, how many pears were there? don't use algebra

Solution

To solve this problem without using algebra, we can use a logical approach by trial and error. Let's break it down step by step:

  1. Assume all 130 fruits were apples:

    • The cost would be 130×0.60=78130 \times 0.60 = 78 dollars.
    • But the total cost is $88, so the difference is 8878=1088 - 78 = 10 dollars.
  2. Now, replace some apples with pears:

    • Each pear costs $0.20 more than an apple.
    • To make up the $10 difference, divide the difference by $0.20: 100.20=50\frac{10}{0.20} = 50
    • So, you would need to replace 50 apples with 50 pears.
  3. Conclusion:

    • There were 50 pears and 13050=80130 - 50 = 80 apples.

So, there were 50 pears.

Would you like more details on this or have any questions? Here are 5 related questions you might find interesting:

  1. What if the cost per apple was $0.50 and per pear was $1.00?
  2. How would the solution change if the total number of fruits was 150 instead of 130?
  3. What if the total cost was $100 instead of $88?
  4. How would you solve it if pears cost $1.20 and apples $0.80?
  5. How can we solve similar problems using a table or diagram?

Tip: In problems like these, finding the difference in cost per item helps to determine the number of one type that needs to be substituted for another.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Problem Solving

Formulas

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Theorems

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Suitable Grade Level

Grades 5-6