A zoo has lions and tigers. A sign states that there are 3 times as many tigers as lions. A...

1. TRANSLATE the problem information

• Given information:
  • There are 3 times as many tigers as lions
  • Total lions and tigers = 400
  • Need to find: number of lions

• What this tells us:
  • If \(\mathrm{L = lions}\) and \(\mathrm{T = tigers}\), then \(\mathrm{T = 3L}\)
  • Also \(\mathrm{T + L = 400}\)

2. INFER the solution approach

• We have a system of two equations with two unknowns
• Since one equation already expresses T in terms of L, substitution is the most direct method
• Strategy: Replace T in the second equation with 3L

3. SIMPLIFY using substitution

• Substitute \(\mathrm{T = 3L}\) into \(\mathrm{T + L = 400}\):
  \(\mathrm{3L + L = 400}\)
• Combine like terms: \(\mathrm{4L = 400}\)
• Divide both sides by 4: \(\mathrm{L = 100}\)

4. Verify the answer

• If \(\mathrm{L = 100}\), then \(\mathrm{T = 3(100) = 300}\)
• Check: \(\mathrm{100 + 300 = 400}\) ✓

Answer: A (100)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students mix up which animal has more, setting up \(\mathrm{L = 3T}\) instead of \(\mathrm{T = 3L}\).

When they see "3 times as many tigers as lions," they might think "lions = 3 × tigers" instead of "tigers = 3 × lions." This leads to the system \(\mathrm{L = 3T}\) and \(\mathrm{L + T = 400}\), which gives \(\mathrm{T = 100}\) and \(\mathrm{L = 300}\).

This may lead them to select Choice D (300).

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when combining terms or solving equations.

They might incorrectly combine 3L + L as 3L instead of 4L, or make division errors when solving \(\mathrm{4L = 400}\). These calculation mistakes can lead to various incorrect values.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

The key challenge is carefully interpreting the relationship "3 times as many tigers as lions" and translating it correctly into mathematical notation. Once the system is set up properly, the algebra is straightforward.