Art of Problem Solving

2009 CEMC Gauss (Grade 8) Problems/Problem 7: Difference between revisions

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{{CEMC box|year=2009|competition=Gauss (Grade 8)|num-b=6|num-a=8}}

Latest revision as of 20:11, 19 October 2025

Problem

Kayla went to the fair with $\$100$. She spent $\frac14$ of her $\$100$ on rides, and $\frac{1}{10}$ of her $\$100$ on food. How much money did she spend?

$\text{ (A) }\ \$65 \qquad\text{ (B) }\ \$32.50 \qquad\text{ (C) }\ \$2.50 \qquad\text{ (D) }\ \$50 \qquad\text{ (E) }\ \$35$

Solution 1

We can calculate how much she spent on her rides, then the amount she spent on food, and then add them together.

For the rides, she spent:

$\frac14 \times \$100 = \$25$

For the food, she spent:

$\frac{1}{10} \times \$100 = \$10$

Thus, altogether, she spent:

$\$25 + \$10 = \boxed {\textbf {(E) } \$35}$

~anabel.disher

Solution 2

We can combine the fractions to see what fraction of the $\$100$ she spent altogether:

$\frac14 + \frac{1}{10} = \frac{1 \times 5}{4 \times 5} + \frac{1 \times 2}{10 \times 2} = \frac{5}{20} + \frac{2}{20} = \frac{7}{20}$

We can now multiply this by the $\$100$ she was given to see how much she spent altogether:

$\frac{7}{20} \times \$100 = \boxed {\textbf {(E) } \$35}$

~anabel.disher

2009 CEMC Gauss (Grade 8) (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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CEMC Gauss (Grade 8)