2007 AMC 12B Problem 5

Problem 5 of 25EasierAlgebra

The

2007

AMC

12

contests will be scored by awarding

6

points for each correct response,

0

points for each incorrect response, and

1.5

points for each problem left unanswered. After looking over the

25

problems, Sarah has decided to attempt the first

22

and leave the last

3

unanswered. How many of the first

22

problems must she solve correctly in order to score at least

100

points?

Show solution

Solution

The three unanswered problems give

3\cdot1.5=4.5

points. So Sarah needs at least

100-4.5=95.5

points from correct answers. Since

15\lt\dfrac{95.5}{6}\lt16,

she must solve at least

16

problems correctly, which would give her

16\cdot6+4.5=100.5

points. Thus, the correct answer is D.