Difference between revisions of "2016 AMC 10A Problems/Problem 3"
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<math>\textbf{(A)}\ \$37.50 \qquad\textbf{(B)}\ \$50.00\qquad\textbf{(C)}\ \$87.50\qquad\textbf{(D)}\ \$90.00\qquad\textbf{(E)}\ \$92.50</math> | <math>\textbf{(A)}\ \$37.50 \qquad\textbf{(B)}\ \$50.00\qquad\textbf{(C)}\ \$87.50\qquad\textbf{(D)}\ \$90.00\qquad\textbf{(E)}\ \$92.50</math> | ||
| − | ==Solution== | + | ==Solution 1== |
If Ben paid <math>\$ 12.50</math> more than David, then he paid <math>\frac{12.5}{.25}= \$ 50.00</math>. Thus, David paid <math>\$ 37.50</math>, and they spent <math>50.00+37.50 =\$ 87.50 \implies \boxed{\textbf{(C) }\$ 87.50}</math>. | If Ben paid <math>\$ 12.50</math> more than David, then he paid <math>\frac{12.5}{.25}= \$ 50.00</math>. Thus, David paid <math>\$ 37.50</math>, and they spent <math>50.00+37.50 =\$ 87.50 \implies \boxed{\textbf{(C) }\$ 87.50}</math>. | ||
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| + | ==Solution 2== | ||
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| + | If for every dollar Ben spent on bagels David spent <math>25</math> cents less, then the ratio of the money that Ben spent to David spent is <math>4:3</math>. We know that Ben paid <math>\$12.50</math> more than David, so we can write <math>\$12.50\cdot (4+3)=\$ 87.50.</math> Then the answer is <math>\boxed{\text{(C)}}.</math> | ||
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| + | ~@azure123456 | ||
| + | |||
| + | ==Video Solution (HOW TO THINK CREATIVELY!!!)== | ||
| + | https://youtu.be/huMBaF16tlM | ||
| + | |||
| + | ~Education, the Study of Everything | ||
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| + | |||
| + | |||
==Video Solution== | ==Video Solution== | ||
https://youtu.be/VIt6LnkV4_w?t=81 | https://youtu.be/VIt6LnkV4_w?t=81 | ||
| − | ~ | + | https://youtu.be/tYU8ZZKar4A |
| + | |||
| + | ~savannahsolver | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2016|ab=A|num-b=2|num-a=4}} | {{AMC10 box|year=2016|ab=A|num-b=2|num-a=4}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 09:58, 16 June 2023
Contents
Problem
For every dollar Ben spent on bagels, David spent 
cents less. Ben paid 
more than David. How much did they spend in the bagel store together?
Solution 1
If Ben paid 
more than David, then he paid 
. Thus, David paid 
, and they spent 
.
Solution 2
If for every dollar Ben spent on bagels David spent cents less, then the ratio of the money that Ben spent to David spent is 
. We know that Ben paid more than David, so we can write 
Then the answer is 
~@azure123456
Video Solution (HOW TO THINK CREATIVELY!!!)
https://youtu.be/huMBaF16tlM
~Education, the Study of Everything
Video Solution
https://youtu.be/VIt6LnkV4_w?t=81
~savannahsolver
See Also
| 2016 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
