1999 AMC 8 Problems/Problem 16

Problem

Tori's mathematics test had 75 problems: 10 arithmetic, 30 algebra, and 35 geometry problems. Although she answered 70% of the arithmetic, 40% of the algebra, and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% of the problems right. How many more problems would she have needed to answer correctly to earn a 60% passing grade?

$\text{(A)}\ 1 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 7 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 11$

Solution

First, calculate how many of each type of problem she got right:

Arithmetic: $70\% \cdot 10 = 0.70 \cdot 10 = 7$

Algebra: $40\% \cdot 30 = 0.40 \cdot 30 = 12$

Geometry: $60\% \cdot 35 = 0.60 \cdot 35 = 21$

Altogether, Tori answered $7 + 12 + 21 = 40$ questions correct. To get a $60\%$ on her test overall, she needed to get $60\% \cdot 75 = 0.60 \cdot 75 = 45$ questions right.

Therefore, she needed to answer $45 - 40 = 5$ more questions to pass, and the the correct answer is $\boxed{B}$

1999 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 15	Followed by Problem 17
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1999 AMC 8 Problems/Problem 16

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