5 less than 4 times a number y is equal to 23. Which equation represents this situation?

1. TRANSLATE the word phrase into mathematical components

• Break down "5 less than 4 times a number y is equal to 23":
  • "4 times a number y" = \(\mathrm{4y}\)
  • "5 less than [something]" means subtract 5 from that something
  • "is equal to 23" = = 23

2. INFER the correct order and structure

• The phrase "5 less than 4 times a number y" means:
  • Start with \(\mathrm{4y}\)
  • Then subtract 5 from it
  • This gives us: \(\mathrm{4y - 5}\)

• Setting this equal to 23: \(\mathrm{4y - 5 = 23}\)

3. TRANSLATE to match answer choices

• Compare \(\mathrm{4y - 5 = 23}\) with the given options:
  • (A) \(\mathrm{5 - 4y = 23}\) ✗ (wrong order)
  • (B) \(\mathrm{4y + 5 = 23}\) ✗ (addition instead of subtraction)
  • (C) \(\mathrm{5y - 4 = 23}\) ✗ (wrong coefficient and constant)
  • (D) \(\mathrm{4y - 5 = 23}\) ✓ (matches our translation)

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students often translate "5 less than 4 times a number y" as "\(\mathrm{5 - 4y}\)" instead of "\(\mathrm{4y - 5}\)"

The confusion comes from reading left to right and thinking "5 less than" means "5 minus something." However, "5 less than X" actually means "\(\mathrm{X - 5}\)," not "\(\mathrm{5 - X}\)." It's like saying "5 less than 10 equals 5," which translates to \(\mathrm{10 - 5 = 5}\).

This may lead them to select Choice A (\(\mathrm{5 - 4y = 23}\)).

Second Most Common Error:

Weak TRANSLATE skill: Students correctly identify the subtraction but get confused about which number is the coefficient of the variable

They might write \(\mathrm{5y - 4 = 23}\), mixing up whether it's "4 times y" or "5 times y" and whether to subtract 4 or 5.

This may lead them to select Choice C (\(\mathrm{5y - 4 = 23}\)).

The Bottom Line:

Word-to-equation translation requires careful attention to phrase structure. "Less than" problems are particularly tricky because the order in English (5 less than X) is opposite to the mathematical order (\(\mathrm{X - 5}\)).