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ratio problem

The ratio of the number of adults to the number of students at the school dance has to be 1:10. Last year there were 477 more students than adults at the dance. If the school is expecting the same attendance this year, how many adults have to attend the dance?

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Rajesh P. | Effective Tutor for Test Prep, Math, Science, Comp Science, BusinessEffective Tutor for Test Prep, Math, Sci...
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-1
Let number of adults attending the dance = a
Let number of students attending the dance = s
 
Given
a/s = 1/10 ....multiply both the sides by 10 s
s = 10a ........(1)
 
There were 477 more students than adults
s = a + 477 ........(2)
 
Substitute (2) into (1)
a + 477 = 10a ....subtract a from both the sides
477 = 9a .....divide both sides by 9
53 = a 
 
So 53 adults have to attend the dance.