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2009 CEMC Gauss (Grade 8) Problems/Problem 14: Difference between revisions

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{{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==
==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?
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?
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~anabel.disher
~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}}

Latest revision as of 20:23, 19 October 2025

The following problem is from both the 2009 CEMC Gauss (Grade 8) #14 and 2009 CEMC Gauss (Grade 7) #17, so both problems redirect to this page.

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

2009 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources)
Preceded by
Problem 13 		Followed by
Problem 15
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
CEMC Gauss (Grade 8)
2009 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources)
Preceded by
Problem 16 		Followed by
Problem 18
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
CEMC Gauss (Grade 7)
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