Difference between revisions of "2019 AMC 10B Problems/Problem 3"
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Thus there are <math>500-x = 220</math> non-seniors. Since 70% of the non-seniors play a musical instrument, <math>220 \cdot \frac{7}{10} = \boxed{B) 154}</math> | Thus there are <math>500-x = 220</math> non-seniors. Since 70% of the non-seniors play a musical instrument, <math>220 \cdot \frac{7}{10} = \boxed{B) 154}</math> | ||
+ | |||
+ | ==Solution 2== | ||
+ | |||
+ | Let x be the number of seniors, and y be the number of non-seniors. Then <cmath>\frac{3}{5}x + \frac{3}{10}y = \frac{468}{1000}\cdot500 = 234</cmath> | ||
+ | |||
+ | Multiplying 10 to every term gives us | ||
+ | <cmath>6x + 3y = 2340</cmath> | ||
+ | |||
+ | Also, <math>x + y = 500</math> because there are 500 students in total. | ||
+ | |||
+ | |||
+ | Solving these system of equations give us <math>x = 280</math>, <math>y = 220</math> | ||
+ | |||
+ | |||
+ | Since 70% of the non-seniors play a musical instrument, we simply get 70% of 220, which gives us <math>\boxed{B) 154}</math> | ||
==See Also== | ==See Also== |
Revision as of 21:18, 15 February 2019
Contents
Problem
In a high school with students, of the seniors play a musical instrument, while of the non-seniors do not play a musical instrument. In all, of the students do not play a musical instrument. How many non-seniors play a musical instrument?
Solution
60% of seniors do not play a musical instrument. If we denote x as the number of seniors, then
Thus there are non-seniors. Since 70% of the non-seniors play a musical instrument,
Solution 2
Let x be the number of seniors, and y be the number of non-seniors. Then
Multiplying 10 to every term gives us
Also, because there are 500 students in total.
Solving these system of equations give us ,
Since 70% of the non-seniors play a musical instrument, we simply get 70% of 220, which gives us
See Also
2019 AMC 10B (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 |
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