Solve the Ratio Problem: Finding Distribution of 80 Items in 3:5:2 Proportion

The solution involves distributing 80 pencils across three cases following a ratio of 3:5:2.

To find the number of pencils in each pencil case, follow these steps:

• Step 1: Calculate the sum of the ratio parts. Here, the sum is $3 + 5 + 2 = 10$.
• Step 2: Calculate the number of pencils per unit of ratio: - Each unit is $\frac{80}{10} = 8$ pencils.
• Step 3: Calculate the number of pencils in each case using the ratio:
  Pencil case A: $3 \times 8 = 24$,
  Pencil case B: $5 \times 8 = 40$,
  Pencil case C: $2 \times 8 = 16$.

Thus, the number of pencils in each case is:

Pencil case A 24 pencils, Pencil case B 40 pencils, Pencil case C 16 pencils