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| − | ==Problem==
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| − | Kayla went to the fair with <math>\$100</math>. She spent <math>\frac14</math> of her <math>\$100</math> on rides, and <math>\frac{1}{10}</math> of her <math>\$100</math> on food. How much money did she spend?
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| − | <math> \text{ (A) }\ \$65 \qquad\text{ (B) }\ \$32.50 \qquad\text{ (C) }\ \$2.50 \qquad\text{ (D) }\ \$50 \qquad\text{ (E) }\ \$35 </math>
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| − | ==Solution 1==
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| − | We can calculate how much she spent on her rides, then the amount she spent on food, and then add them together.
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| − | For the rides, she spent:
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| − | <math>\frac14 \times \$100 = \$25</math>
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| − | For the food, she spent:
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| − | <math>\frac{1}{10} \times \$100 = \$10</math>
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| − | Thus, altogether, she spent:
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| − | <math>\$25 + \$10 = \boxed {\textbf {(E) } \$35}</math>
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| − | ~anabel.disher
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| − | ==Solution 2==
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| − | We can combine the fractions to see what fraction of the <math>\$100</math> she spent altogether:
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| − | <math>\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}</math>
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| − | We can now multiply this by the <math>\$100</math> she was given to see how much she spent altogether:
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| − | <math>\frac{7}{20} \times \$100 = \boxed {\textbf {(E) } \$35}</math>
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| − | ~anabel.disher
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