Difference between revisions of "2009 Grade 8 CEMC Gauss Problems/Problem 7"
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==Problem== | ==Problem== | ||
| − | + | 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? | |
| − | <math> \text{ (A) }\ | + | <math> \text{ (A) }\ \$65 \qquad\text{ (B) }\ \$32.50 \qquad\text{ (C) }\ \$2.50 \qquad\text{ (D) }\ \$50 \qquad\text{ (E) }\ \$35 </math> |
==Solution 1== | ==Solution 1== | ||
| − | We can | + | 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: | |
| − | + | <math>\frac14 \times \$100 = \$25</math> | |
| − | + | For the food, she spent: | |
| − | + | <math>\frac{1}{10} \times \$100 = \$10</math> | |
| − | + | Thus, altogether, she spent: | |
| − | + | <math>\$25 + \$10 = \boxed {\textbf {(E) } \$35}</math> | |
| − | |||
| − | |||
~anabel.disher | ~anabel.disher | ||
==Solution 2== | ==Solution 2== | ||
| − | We can | + | We can combine the fractions to see what fraction of the <math>\$100</math> she spent altogether: |
| + | |||
| + | <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> | ||
| + | |||
| + | We can now multiply this by the <math>\$100</math> she was given to see how much she spent altogether: | ||
| + | |||
| + | <math>\frac{7}{20} \times \$100 = \boxed {\textbf {(E) } \$35}</math> | ||
~anabel.disher | ~anabel.disher | ||
Latest revision as of 23:09, 18 June 2025
Problem
Kayla went to the fair with 
. She spent 
of her on rides, and 
of her on food. How much money did she spend?
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:
For the food, she spent:
Thus, altogether, she spent:
~anabel.disher
Solution 2
We can combine the fractions to see what fraction of the she spent altogether:
We can now multiply this by the she was given to see how much she spent altogether:
~anabel.disher
