A local paint store sells a certain solvent in containers of two sizes--small and large. The capacity, in liters, of...

Phase 1: Owning the Dataset

Visualization

Let's create a simple comparison to understand the relationship:

5 Small containers: [S][S][S][S][S] = Total capacity
2 Large containers: [  L  ][  L  ]  = Same total capacity

This tells us: \(5\mathrm{S} = 2\mathrm{L}\) (where S = small container capacity, L = large container capacity)

Key Relationship

From \(5\mathrm{S} = 2\mathrm{L}\), we can derive:

• \(\mathrm{S} = \frac{2\mathrm{L}}{5}\)
• Each small container holds \(\frac{2}{5}\) the capacity of a large container

Phase 2: Understanding the Question

We need to find two values:

1. Large: The capacity of 1 large container
2. Combined: The capacity of 1 small + 1 large container

Setting Up Our Formula

Combined capacity = \(\mathrm{S} + \mathrm{L} = \frac{2\mathrm{L}}{5} + \mathrm{L} = \frac{2\mathrm{L}}{5} + \frac{5\mathrm{L}}{5} = \frac{7\mathrm{L}}{5}\)

Key insight: The combined capacity must equal \(\frac{7}{5}\) times the large container capacity.

Phase 3: Finding the Answer

We need to find an L value from our choices where \(\frac{7\mathrm{L}}{5}\) is also in the choices.

Let's check systematically:

If L = 45: Combined = \(\frac{7(45)}{5} = \frac{315}{5} = 63\) (not in choices)

If L = 50: Combined = \(\frac{7(50)}{5} = \frac{350}{5} = 70\) ✓ (70 is in choices!)

? Stop here - we found our answer.

Verification

• Large container: 50 liters
• Small container: \(\frac{2(50)}{5} = 20\) liters
• Combined: 20 + 50 = 70 liters ✓
• Check original condition: \(5(20) = 100\) and \(2(50) = 100\) ✓

Phase 4: Solution

Large: 50
Combined: 70

The large container holds 50 liters, and the combined capacity of one small and one large container is 70 liters.