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>. | ||
+ | |||
+ | ==Solution 2== | ||
+ | |||
+ | 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> | ||
+ | |||
+ | ~@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 | ||
+ | |||
+ | 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
[hide]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 |
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