2007 AMC 10B Problem 6

Problem 6 of 25EasierAlgebra

The

2007

AMC

10

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 only 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 blank problems give

3\cdot 1.5 = 4.5

points, so Sarah needs

100-4.5=95.5

points from the first

22.

Since

\frac{95.5}{6}

lies between

15

and

16,

she must answer at least

16

correctly, which would give a score of

100.5.

Thus, the correct answer is D.