2009 Grade 8 CEMC Gauss Problems/Problem 14

Problem

Vanessa set a school record for the most points in a single basketball game when her team scored $48$ points. The other six players on her team averaged $3.5$ points each. How many points did Vanessa score to set her school record?

$\text{ (A) }\ 21 \qquad\text{ (B) }\ 25 \qquad\text{ (C) }\ 32 \qquad\text{ (D) }\ 17 \qquad\text{ (E) }\ 27$

Solution

We can subtract the number of points that the other six team members got from the total number of points that the team got.

Let $n$ be the number of points that the other six team members got. We can now set up an equation using the average given in the problem:

$\frac{n}{6} = 3.5$

Multiplying both sides by $6$ to get rid of the fraction, we get:

$n = 3.5 \times 6 = 21$

We can now subtract this from the total number of points that the team got, to get how many points Vanessa scored:

$48 - 21 = \boxed {\textbf {(E) } 27}$

~anabel.disher

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2009 Grade 8 CEMC Gauss Problems/Problem 14

Problem

Solution