Difference between revisions of "2016 AMC 10A Problems/Problem 3"
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| + | ==Problem== | ||
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For every dollar Ben spent on bagels, David spent <math>25</math> cents less. Ben paid <math>\$12.50</math> more than David. How much did they spend in the bagel store together? | For every dollar Ben spent on bagels, David spent <math>25</math> cents less. Ben paid <math>\$12.50</math> more than David. How much did they spend in the bagel store together? | ||
<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== | ||
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| + | 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>. | ||
| + | |||
| + | ==Video Solution== | ||
| + | https://youtu.be/VIt6LnkV4_w?t=81 | ||
| + | |||
| + | ~IceMatrix | ||
| + | |||
| + | https://youtu.be/tYU8ZZKar4A | ||
| + | |||
| + | ~savannahsolver | ||
| + | |||
| + | ==See Also== | ||
| + | {{AMC10 box|year=2016|ab=A|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Revision as of 17:18, 16 June 2020
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
If Ben paid 
more than David, then he paid 
. Thus, David paid 
, and they spent 
.
Video Solution
https://youtu.be/VIt6LnkV4_w?t=81
~IceMatrix
~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. 
