Difference between revisions of "2013 AMC 10A Problems/Problem 10"
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− | ==Solution== | + | ==Solution 1== |
Let the total amount of flowers be <math>x</math>. Thus, the number of pink flowers is <math>0.6x</math>, and the number of red flowers is <math>0.4x</math>. The number of pink carnations is <math>\frac{2}{3}(0.6x) = 0.4x</math> and the number of red carnations is <math>\frac{3}{4}(0.4x) = 0.3x</math>. Summing these, the total number of carnations is <math>0.4x+0.3x=0.7x</math>. Dividing, we see that <math>\frac{0.7x}{x} = 0.7 = \boxed{\textbf{(E) }70\%}</math> | Let the total amount of flowers be <math>x</math>. Thus, the number of pink flowers is <math>0.6x</math>, and the number of red flowers is <math>0.4x</math>. The number of pink carnations is <math>\frac{2}{3}(0.6x) = 0.4x</math> and the number of red carnations is <math>\frac{3}{4}(0.4x) = 0.3x</math>. Summing these, the total number of carnations is <math>0.4x+0.3x=0.7x</math>. Dividing, we see that <math>\frac{0.7x}{x} = 0.7 = \boxed{\textbf{(E) }70\%}</math> | ||
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+ | ==Solution 2== | ||
+ | we have <math>\dfrac15</math> for pink roses,<math>1-\dfrac6{10}=4\dfrac{10}=\dfrac25</math> red flowers, <math>\dfrac6{10}-\dfrac15=\dfrac35-\dfrac15=\dfrac25</math> pink carnations, <math>\dfrac25\cdot \dfrac34=\dfrac6{20}=\dfrac3{10}</math> red carnations we add them up to get <math>\dfrac25+\dfrac3{10}=\dfrac7{10}=70\%</math> so our final answer is [u][b]70%[/b][/u | ||
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+ | ~jimkey17 from web2.0calc.com | ||
==See Also== | ==See Also== |
Revision as of 14:55, 30 July 2020
Contents
[hide]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?
Solution 1
Let the total amount of flowers be . Thus, the number of pink flowers is , and the number of red flowers is . The number of pink carnations is and the number of red carnations is . Summing these, the total number of carnations is . Dividing, we see that
Solution 2
we have for pink roses, red flowers, pink carnations, red carnations we add them up to get so our final answer is [u][b]70%[/b][/u
~jimkey17 from web2.0calc.com
See Also
2013 AMC 10A (Problems • Answer Key • Resources) | ||
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 (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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.