Difference between revisions of "2013 AMC 10A Problems/Problem 10"

(Solution 2)
 
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~jimkey17 from web2.0calc.com
 
~jimkey17 from web2.0calc.com
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==Video Solution==
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https://www.youtube.com/watch?v=2vf843cvVzo?t=290
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 +
~sugar_rush
  
 
==See Also==   
 
==See Also==   

Latest revision as of 22:20, 23 November 2020

Problem

A flower bouquet contains pink roses, red roses, pink carnations, and red carnations. One third of the pink flowers are roses, three fourths of the red flowers are carnations, and six tenths of the flowers are pink. What percent of the flowers are carnations?


$\textbf{(A)}\ 15 \qquad\textbf{(B)}\ 30  \qquad\textbf{(C)}\ 40 \qquad\textbf{(D)}\ 60 \qquad\textbf{(E)}\ 70$


Solution 1

Let the total amount of flowers be $x$. Thus, the number of pink flowers is $0.6x$, and the number of red flowers is $0.4x$. The number of pink carnations is $\frac{2}{3}(0.6x) = 0.4x$ and the number of red carnations is $\frac{3}{4}(0.4x) = 0.3x$. Summing these, the total number of carnations is $0.4x+0.3x=0.7x$. Dividing, we see that $\frac{0.7x}{x} = 0.7 = \boxed{\textbf{(E) }70\%}$

Solution 2

We have $\dfrac15$ for pink roses,$1-\dfrac6{10}=4\dfrac{10}=\dfrac25$ red flowers, $\dfrac6{10}-\dfrac15=\dfrac35-\dfrac15=\dfrac25$ pink carnations, $\dfrac25\cdot \dfrac34=\dfrac6{20}=\dfrac3{10}$ red carnations we add them up to get $\dfrac25+\dfrac3{10}=\dfrac7{10}=70\%$ so our final answer is 70% or $\boxed{(E)70\%}$

~jimkey17 from web2.0calc.com

Video Solution

https://www.youtube.com/watch?v=2vf843cvVzo?t=290

~sugar_rush

See Also

2013 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
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
2013 AMC 12A (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 12 Problems and Solutions

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