Math Problem Statement

A box of fruits contains 25 fruits, 60% of the apples were sold, and 48% of all the fruits in the box were sold. Determine the number of apples in the box.

Solution

Let’s analyze the problem from the image.

Problem Statement:

  • A box of fruits contains apples and oranges.
  • The total number of fruits is 25.
  • 60% of the apples were sold.
  • A total of 48% of all the fruits in the box were sold.
  • You need to determine the number of apples in the box.

Solution:

Let the number of apples be xx.
Then the number of oranges will be 25x25 - x.

Step 1: Total fruits sold

The problem states that 48% of all the fruits were sold. Since there are 25 fruits: Total fruits sold=48%×25=0.48×25=12.\text{Total fruits sold} = 48\% \times 25 = 0.48 \times 25 = 12.

Step 2: Apples sold

It is also given that 60% of the apples were sold: Apples sold=60%×x=0.6x.\text{Apples sold} = 60\% \times x = 0.6x.

Step 3: Oranges sold

Since the total fruits sold is 12, the number of oranges sold is: Oranges sold=Total fruits soldApples sold=120.6x.\text{Oranges sold} = \text{Total fruits sold} - \text{Apples sold} = 12 - 0.6x.

Step 4: Oranges sold relation

All the oranges must have been sold (as implied). Therefore: Oranges sold=25x.\text{Oranges sold} = 25 - x. Substituting: 120.6x=25x.12 - 0.6x = 25 - x.

Step 5: Solve for xx

Simplify the equation: 120.6x=25x,12 - 0.6x = 25 - x, 1225=x+0.6x,12 - 25 = -x + 0.6x, 13=0.4x,-13 = -0.4x, x=130.4=32.5.x = \frac{13}{0.4} = 32.5.

So number of **apples ____,

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Math Problem Analysis

Mathematical Concepts

Algebra
Percentages

Formulas

Total fruits sold = 48% × Total fruits
Apples sold = 60% × Number of apples
Oranges sold = Total fruits sold - Apples sold

Theorems

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Suitable Grade Level

Grades 6-8