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Difficulty: HardPercents and Percent Change

At a certain car dealership, the number of hybrid vehicles sold in 2024 was 40%40\% of the number of gasoline vehicles sold in 2024. In 2025, the number of hybrid vehicles sold increased by 35%35\% compared to 2024, and the number of gasoline vehicles sold decreased by 10%10\% compared to 2024. If the dealership only sold hybrid and gasoline vehicles in both years, what percent of the total vehicles sold in 2025 were hybrid vehicles?

Answer: 37.5 %

Answer

37.5
To find the percentage of hybrid vehicles sold in 2025, we first express the number of vehicles sold in 2024 in terms of a single variable. Let the number of gasoline vehicles sold in 2024 be gg. Since the hybrid sales were 40%40\% of the gasoline sales, the number of hybrid vehicles sold in 2024 is 0.40g0.40g. In 2025, hybrid sales increased by 35%35\%, resulting in 0.40g×1.35=0.54g0.40g \times 1.35 = 0.54g hybrid vehicles sold. Gasoline sales decreased by 10%10\%, resulting in g×0.90=0.90gg \times 0.90 = 0.90g gasoline vehicles sold. The total number of vehicles sold in 2025 is the sum of these two quantities: 0.54g+0.90g=1.44g0.54g + 0.90g = 1.44g. The percentage of hybrid vehicles sold in 2025 is the ratio of hybrid sales to total sales: 0.54g1.44g×100=37.5%\frac{0.54g}{1.44g} \times 100 = 37.5\%.

Step-by-Step Solution

1
Define variables for the number of vehicles sold in 2024.
Let the number of gasoline vehicles sold in 2024 be gg. The number of hybrid vehicles sold in 2024 is 0.40g0.40g.
Establishing initial values in terms of a single variable allows for comparison after percentage changes are applied.
2
Determine the number of hybrid and gasoline vehicles sold in 2025 after their respective percentage changes.
Hybrid vehicles sold in 2025: 0.40g×(1+0.35)=0.54g0.40g \times (1 + 0.35) = 0.54g. Gasoline vehicles sold in 2025: g×(1−0.10)=0.90gg \times (1 - 0.10) = 0.90g.
Applying the percent increase of 35%35\% to the 2024 hybrid vehicles and the percent decrease of 10%10\% to the 2024 gasoline vehicles.
3
Calculate the total number of vehicles sold in 2025.
Total vehicles sold in 2025: 0.54g+0.90g=1.44g0.54g + 0.90g = 1.44g.
Summing the two types of vehicles sold in 2025 to find the new total.
4
Compute the percentage of hybrid vehicles out of the total vehicles sold in 2025.
0.54g1.44g×100=37.5%\frac{0.54g}{1.44g} \times 100 = 37.5\%.
Dividing the 2025 hybrid sales by the total 2025 sales and multiplying by 100 to convert to a percentage.

Key Concept

Calculating percent change and conditional percentages from initial relative ratios.
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Topics

Percents and Percent Change

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