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==
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==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
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==Video Solution (HOW TO THINK CREATIVELY!!!)==
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https://youtu.be/huMBaF16tlM
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~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
 
~IceMatrix
 
  
 
https://youtu.be/tYU8ZZKar4A
 
https://youtu.be/tYU8ZZKar4A

Latest revision as of 09:58, 16 June 2023

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 1

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

Solution 2

If for every dollar Ben spent on bagels David spent $25$ cents less, then the ratio of the money that Ben spent to David spent is $4:3$. We know that Ben paid $$12.50$ more than David, so we can write $$12.50\cdot (4+3)=$ 87.50.$ Then the answer is $\boxed{\text{(C)}}.$

~@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

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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