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{\textbf{(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{\textbf{(B) } 154}</math>. | ||
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==Solution 2== | ==Solution 2== | ||
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Since <math>70\%</math> of the non-seniors play a musical instrument, the answer is simply <math>70\%</math> of <math>220</math>, which gives us <math>\boxed{\textbf{(B) } 154}</math>. | Since <math>70\%</math> of the non-seniors play a musical instrument, the answer is simply <math>70\%</math> of <math>220</math>, which gives us <math>\boxed{\textbf{(B) } 154}</math>. | ||
− | == Solution 3 ( | + | == Solution 3 (using the answer choices) == |
− | We can clearly deduce that 70% of the non-seniors do play an instrument | + | We can clearly deduce that <math>70\%</math> of the non-seniors do play an instrument, but, since the total percentage of instrument players is <math>46.8\%</math>, the non-senior population is quite low. By intuition, we can therefore see that the answer is around <math>\text{B}</math> or <math>\text{C}</math>. Testing both of these gives us the answer <math>\boxed{\textbf{(B) } 154}</math>. |
==See Also== | ==See Also== |
Revision as of 22:16, 17 February 2019
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 1
of seniors do not play a musical instrument. If we denote
as the number of seniors, then
Thus there are non-seniors. Since 70% of the non-seniors play a musical instrument,
.
Solution 2
Let be the number of seniors, and
be the number of non-seniors. Then
Multiplying both sides by gives us
Also, because there are 500 students in total.
Solving this system of equations give us ,
.
Since of the non-seniors play a musical instrument, the answer is simply
of
, which gives us
.
Solution 3 (using the answer choices)
We can clearly deduce that of the non-seniors do play an instrument, but, since the total percentage of instrument players is
, the non-senior population is quite low. By intuition, we can therefore see that the answer is around
or
. Testing both of these gives us the answer
.
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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