Question

A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

• A. 15
• B. 20
• C. 30
• D. 40
• E. 45

Hint:

In set problems, break down the total into smaller groups and use variables to represent the unknowns.

Answer 1

The Correct Option is B

Step 1: Set up the relationship between groups.
Let \( x \) be the number of households that used both brands of soap. According to the problem, for every household that used both brands, 3 used only Brand B soap. Thus, the number of households that used only Brand B soap is \( 3x \).
Step 2: Use the total number of households surveyed.
We know that:
- 80 households used neither soap.
- 60 households used only Brand A soap.
- \( x \) households used both brands of soap.
- \( 3x \) households used only Brand B soap.
Thus, the total number of households surveyed is: \[ 80 + 60 + x + 3x = 200 \] Solving for \( x \): \[ 80 + 60 + 4x = 200 \implies 140 + 4x = 200 \implies 4x = 60 \implies x = 15 \] \[ \boxed{20} \]