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Question 998487: As a part of the learning journeys program, 73 pupil travel on 2 buses, 1 air conditioned and 1 non air conditioned to the Singapore discovery center, three- fifths of the people in the air conditioned 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 pupil were on the air conditioned bus??
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number of people on the bus with air conditioning.
let y = the number of people on the bus without air conditioning.
the number of girls on the bus with air conditioning is 3/5 * x
the number of girls on the bus without air conditioning is also 3/5 * x, because there is an equal number of girls on both buses.
the number of boys on the bus with air conditioning is 2/5 * x, because 3/5 * x + 2/5 * x = 5/5 * x = x. 3/5 * x are girls, so 2/5 * x must be boys.
the total number of boys and girls on both buses is equal to 73.
the total number of boys on both buses is 2/5 * x + 17.
the total number of girls on both buses is (3/5 * x + 3/5 * x) = 6/5 * x
add them together and you get total of boys and girls on both buses is 8/5 * x + 17.
since the total of boys and girls on both buses is 73, then you get:
8/5 * x + 17 = 73.
subtract 17 from both sides of this equation to get:
8/5 * x = 56
divide both sides of this equation by 8 and multiply both sides of this equation by 5 and you get x = 56 * 5 / 8 = 35.
x = 35.
that represents the total number of boys and girls on the bus with air conditioning.
that means the total number of boys and girls on the bus without air conditioning must be 73 - 35 = 38, because the total number of pupils on both buses is 73.
you were asked how many pupils were on the bus with air conditoning.
that would be 35.
the formulas and the numbers can be summarized in a table like this:
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formulas:
bus with AC bus without AC Total on both buses
boys 2/5 * x 17 2/5 * x + 17
girls 3/5 * x 3/5 * x 6/5 * x
Total on each bus 5/5 * x 3/5 * x + 17 8/5 * x + 17
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numbers:
bus with AC bus without AC Total on both buses
boys 14 17 31
girls 21 21 42
Total on each bus 35 38 73
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