Question

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?

$1$

$5$

$7$

$9$

$11$

Solution:

She answered $10 \cdot .7 = 7$ arithmetic questions correctly. She answered $30 \cdot .4 = 12$ algebra ones correctly. She also got $35 \cdot .6 = 21$ geometry questions correctly.

This means she got a total of $7 + 12 + 21 = 40$ questions correct.

As such, in order to get a $60\%,$ Tori must have answered $75 \cdot .6 = 45$ questions correctly. This means that she would have needed to answer an additional $45 - 40 = 5$ questions correctly.

Thus, B is the correct answer.

1999 AMC 8 Problem 16

Solution:

Problem 16 in Other Years