A water tank contains an amount of water w (in gallons) that is 25 gallons less than half the tank's...

1. TRANSLATE the problem information

• Given information:
  • Water amount w is "25 gallons less than half the tank's total capacity c"
  • Need to find the equation relating w and c

2. TRANSLATE each part of the description

• Break down the phrase step by step:
  • "half the tank's total capacity c" → \(\mathrm{c/2}\)
  • "25 gallons less than" this amount → subtract 25 from \(\mathrm{c/2}\)
  • Complete translation: \(\mathrm{w = c/2 - 25}\)

3. INFER the correct mathematical structure

• The phrase "25 gallons less than [something]" means:
  • Start with that "something" (which is \(\mathrm{c/2}\))
  • Then subtract 25 from it
  • This gives us \(\mathrm{c/2 - 25}\), not \(\mathrm{25 - c/2}\)

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret "25 gallons less than" as meaning addition rather than subtraction.

They think "less than" somehow means "plus" and write \(\mathrm{w = c/2 + 25}\).

This may lead them to select Choice A (\(\mathrm{w = c/2 + 25}\))

Second Most Common Error:

Poor TRANSLATE reasoning: Students get the order of subtraction backwards in the phrase "25 gallons less than half the capacity."

They correctly identify that subtraction is needed, but think the phrase means "25 minus half the capacity" instead of "half the capacity minus 25," writing \(\mathrm{w = 25 - c/2}\).

This may lead them to select Choice D (\(\mathrm{w = 25 - c/2}\))

The Bottom Line:

The key challenge is carefully parsing the English phrase "X less than Y" to mean "\(\mathrm{Y - X}\)" in mathematical notation, not "\(\mathrm{X - Y}\)" or "\(\mathrm{X + Y}\)."