View source for 2009 CEMC Gauss (Grade 8) Problems/Problem 14

{{Duplicate|[[2009 CEMC Gauss (Grade 8) Problems|2009 CEMC Gauss (Grade 8) #14]] and [[2009 CEMC Gauss (Grade 7) Problems|2009 CEMC Gauss (Grade 7) #17]]}}
==Problem==
Vanessa set a school record for the most points in a single basketball game when her team scored <math>48</math> points. The other six players on her team averaged <math>3.5</math> points each. How many points did Vanessa score to set her school record?

<math> \text{ (A) }\ 21 \qquad\text{ (B) }\ 25 \qquad\text{ (C) }\ 32 \qquad\text{ (D) }\ 17 \qquad\text{ (E) }\ 27 </math>
==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 <math>n</math> 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:

<math>\frac{n}{6} = 3.5</math>

Multiplying both sides by <math>6</math> to get rid of the fraction, we get:

<math>n = 3.5 \times 6 = 21</math>

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

<math>48 - 21 = \boxed {\textbf {(E) } 27}</math>

~anabel.disher
{{CEMC box|year=2009|competition=Gauss (Grade 8)|num-b=13|num-a=15}}
{{CEMC box|year=2009|competition=Gauss (Grade 7)|num-b=16|num-a=18}}