2003 AMC 8 Problems/Problem 7

Problem

Blake and Jenny each took four $100$ -point tests. Blake averaged $78$ on the four tests. Jenny scored $10$ points higher than Blake on the first test, $10$ points lower than him on the second test, and $20$ points higher on both the third and fourth tests. What is the difference between Jenny's average and Blake's average on these four tests?

$\mathrm{(A)}\ 10 \qquad\mathrm{(B)}\ 15 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 25 \qquad\mathrm{(E)}\ 40$

Solution

Solution 1

Blake scored a total of $4 \times 78=312$ points. Jenny scored $10-10+20+20=40$ points higher than Blake, so her average is $\frac{312+40}{4}=88$ . the difference is $88-78=\boxed{\mathrm{(A)}\ 10}$ .

Solution 2

The total point difference between Blake's and Jenny's scores is $10-10+20+20=40$ . The average of it is $\frac{40}{4}=\boxed{\mathrm{(A)}\ 10}$ .

2003 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2003 AMC 8 Problems/Problem 7

Contents

Problem

Solution

Solution 1

Solution 2

See Also