Answer to Question #92178 in Algebra for Yami

Question

1000 people entered a math contest to see how many questions out of 20 they could answer correctly in 5 minutes. 15% of them answered 12 questions correctly, three-fifths of them answered 15 questions correctly, and the rest answered 18 questions correctly. What was the percent correct that everyone earned in this contest

Answer 1

1) Number of people:

$$1000(0.15)=150$$

Proportion of correct questions:

$$\frac{12}{20}=0.6$$

2) Number of people:

$$1000 \cdot \frac{3}{5}=600$$

Proportion of correct questions:

$$\frac{15}{20}=0.75$$

3)Number of people:

$$1000-150-600=250$$

Proportion of correct questions:

$$\frac{18}{20}=0.9$$

The proportion correct that everyone earned in this contest:

$$\frac{(150)(0.6)+(600)(0.75)+(250)(0.9)}{1000}=0.765$$

The percent correct that everyone earned in this contest is 76.5%.