The product of 4 and a number y is 144. What is the value of y?

1. TRANSLATE the problem information

• Given information: "The product of 4 and a number y is 144"
• In mathematical notation: \(\mathrm{4y = 144}\)
• What this tells us: We have a simple linear equation to solve

2. INFER the solution strategy

• To find y, we need to isolate the variable
• Since y is being multiplied by 4, we use the inverse operation (division)
• We'll divide both sides by 4 to maintain equality

3. SIMPLIFY to find the answer

• Divide both sides by 4: \(\mathrm{4y ÷ 4 = 144 ÷ 4}\)
• This gives us: \(\mathrm{y = 36}\)
• Double-check: \(\mathrm{4 × 36 = 144}\) ✓

Answer: B) 36

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may misinterpret "product" and think it means addition instead of multiplication, setting up the equation as \(\mathrm{4 + y = 144}\). When they solve this, they get \(\mathrm{y = 140}\), which leads them to select Choice C (140).

Second Most Common Error:

Poor arithmetic execution: Students correctly set up \(\mathrm{4y = 144}\) but make a division error when calculating \(\mathrm{144 ÷ 4}\), perhaps getting confused with the numbers and calculating incorrectly. This leads to confusion and potential guessing among the remaining choices.

The Bottom Line:

This problem tests the fundamental skill of translating word problems into algebraic equations. The word "product" is the key - students who don't immediately recognize it means multiplication will struggle from the very beginning.