2009 Grade 8 CEMC Gauss Problems/Problem 7

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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