GMAT Practice Question: Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on...
Question
Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50 percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4 percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items, then the total tax that she paid was what percent of the total amount that she spent, excluding taxes?
- 2.8 \%
- 3.6 \%
- 4.4 \%
- 5.2 \%
- 6.0 \%
Topics: word problems, percentages, translations
Solution
Step 1
We first create a variable for the total pre-tax spending, letting T represent this amount.
T=\text{total pre-tax spending}
Step 2
We translate the spending percentages from the question into decimal expressions: \textbf{\text{"50 percent"}}, \textbf{\text{"20 percent"}}, and \textbf{\text{"30 percent"}} of T.
\text{Clothing}=\frac{50}{100}T=0.5T \text{Food}=\frac{20}{100}T=0.2T \text{Other}=\frac{30}{100}T=0.3T
Step 3
We translate the tax rates from the question into decimal multipliers: \textbf{\text{"4 percent tax on the clothing"}}, \textbf{\text{"no tax on the food"}}, and \textbf{\text{"8 percent tax on all other items"}}.
\text{Tax on clothing}=0.04\times0.5T=0.02T \text{Tax on food}=0\times0.2T=0 \text{Tax on other}=0.08\times0.3T=0.024T
Step 4
We add the taxes and convert to a percentage of T.
\text{Total tax}=0.02T+0.024T=0.044T \frac{\text{Total tax}}{T}\times100\%=0.044\times100\%=4.4\%
Answer
4.4%
