2001 CEMC Pascal Problems/Problem 10

Problem

Dean scored a total of $252$ points in $18$ basketball games. Ruth played $10$ fewer games than Dean. Her scoring average was $0.5$ points per game higher than Dean's scoring average. How many points, in total, did Ruth score?

$\text{ (A) }\ 153 \qquad\text{ (B) }\ 171 \qquad\text{ (C) }\ 180 \qquad\text{ (D) }\ 266 \qquad\text{ (E) }\ 144$

Solution

We can first find Dean's average and use it to find the average of Ruth's points, the number of games that Ruth played, then use that to find out how many points Ruth had in total.

Dean's average was $\frac{252}{28} = 9$ points per game. Since Ruth's average was $0.5$ points higher, her average was $9 + 0.5 = 9.5$ .

Since Dean played $28$ games, Ruth played $28 - 10 = 18$ games.

The number of points that Ruth got was then $9.5 \times 18 = \frac{19}{2} \times 18 = \boxed {\textbf {(B) } 171}$

~anabel.disher

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2001 CEMC Pascal Problems/Problem 10

Problem

Solution