The density of a substance is the mass of the substance per unit volume. A sample of liquid has a...

1. TRANSLATE the problem information

• Given information:
  • Mass = 105 grams
  • Density = 15 grams per cubic centimeter
  • Need to find: Volume in cubic centimeters
• The problem also provides the key formula: \(\mathrm{Density = \frac{Mass}{Volume}}\)

2. TRANSLATE the relationship into an equation

• Substitute the known values into the density formula:
  \(\mathrm{15 = \frac{105}{Volume}}\)

3. INFER the solving strategy

• To find Volume, we need to rearrange this equation
• Since Volume is in the denominator, we need to isolate it

4. SIMPLIFY through algebraic manipulation

• Multiply both sides by Volume: \(\mathrm{15 \times Volume = 105}\)
• Divide both sides by 15: \(\mathrm{Volume = 105 \div 15}\)
• Calculate: \(\mathrm{Volume = 7}\)

Answer: A. 7

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students recognize they need to use the density formula but get confused about which operation to perform with the numbers. Instead of dividing mass by density, they might multiply the given numbers together.

This reasoning leads them to calculate \(\mathrm{105 \times 15 = 1575}\), causing them to select Choice D (1575).

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand the relationship between the quantities and think they should add or subtract the given values rather than use the density formula.

For example, they might calculate \(\mathrm{105 + 15 = 120}\) or \(\mathrm{105 - 15 = 90}\), leading them to select Choice C (120) or Choice B (90).

The Bottom Line:

This problem tests whether students can properly apply the density formula and resist the temptation to simply perform arithmetic with the given numbers without considering their mathematical relationship.