SOLUTION: As part of the 'learning journey'program, 73 pupils travelled on two buses, one air-conditioned and one non-air-conditioned, to the Singapore Discovery Centre. Three-fifths of the

Question 432428: As part of the 'learning journey'program, 73 pupils travelled on two buses, one air-conditioned and one non-air-conditioned, to the Singapore Discovery Centre. Three-fifths of the pupils on the air-conditoned bus were girls. There were 17 boys in the non-air conditioned bus. The number of girls on the two buses were equal. How many pupils were there on the air-conditioned bus?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let t = the total number of students on the air-conditioned bus (#1)
Then 73-t = the total number on the non-air-conditioned bus (#2)
Let b = the number of boys on the air-conditioned bus
Let g = the number of girls (the same on both buses)
Since 3/5 of the students are girls, we can write the following equation for bus #1:
g = 3/5t (1)
There are 17 boys on bus #2, so we can write the following for bus #2:
73 - t = 17 + g (2)
Now we have 2 equations and 2 unknowns.
Substituting the value for g from (1) into (2) gives:
73 - t = 17 + (3/5)t
Solve for t:
(8/5)t = 56 -> t = 35
So there are 35 pupils on the air-conditioned bus.
Check:
The number of girls = 3/5*35 = 21
The number of boys on bus #1 = 73 - 21 - 21 - 17 = 14
And since 2/5 of the pupils on bus #1 are boys:
2/5*35 = 14

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