2003 AMC 8 Problems/Problem 7

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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 $\frac{40}{4}=\boxed{\mathrm{(A)}\ 10}$.

See Also

2003 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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