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>
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==Solution==
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If Ben paid <math>\$ 12.50</math> more than David, then he paid <math>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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==See Also==
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{{AMC10 box|year=2016|ab=A|num-b=2|num-a=4}}
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{{MAA Notice}}

Revision as of 18:26, 3 February 2016

Problem

For every dollar Ben spent on bagels, David spent $25$ cents less. Ben paid $$12.50$ more than David. How much did they spend in the bagel store together?

$\textbf{(A)}\ $37.50 \qquad\textbf{(B)}\ $50.00\qquad\textbf{(C)}\ $87.50\qquad\textbf{(D)}\ $90.00\qquad\textbf{(E)}\ $92.50$

Solution

If Ben paid $$ 12.50$ more than David, then he paid $12.5/.25=$ 50.00$. Thus, David paid $$ 37.50$, and they spent $50.00+37.50 =$ 87.50 \implies \boxed{\textbf{(C) }$ 87.50}$.

See Also

2016 AMC 10A (ProblemsAnswer KeyResources)
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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