SOLUTION: Please help me solve this problem:
At station A, the number of adults was 25% fewer than the number of children on a train. At station B, 25 children alighted from the train and
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Question 896691: Please help me solve this problem:
At station A, the number of adults was 25% fewer than the number of children on a train. At station B, 25 children alighted from the train and 25 adults boarded the train. There were then 100% more adults than children. How many adults were on the train when it left station B?
Thanks heaps!
Found 2 solutions by josmiceli, Theo:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Instead of percents, use fractions
25% =
100% =
--------------
Let = number of adults on train
Let = number of children on train
--------------
At station A:
(1)
At station B:
children are left
adults on train
(2)
-----------------------------------
(1)
(1)
(1)
--------------------
(2)
(2)
By substitution:
(2)
(2)
(2)
(2)
(2)
----------------
When the train left station B, there were
adults on board
--------------------------------
check:
(1)
(1)
(1)
(1)
(1)
and
(2)
(2)
(2)
(2)
(2)
OK
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a = number of adults.
let c = number of children.
at station A you get:
a = c - .25c which results in a = .75c
at station B you get:
(a+25) = 2 * (c-25)
from the equation for station a, you can replace a with .75c in the equation for station B to get:
(.75c + 25) = 2 * (c - 25)
simplify this to get:
.75c + 25 = 2c - 50
subtract .75c from both sides of the equation and add 50 to both sides of the equation to get:
75 = 1.25c
divide both sides of the equation by 1.25 to get:
c = 60
at station A, then a must be equal to 45 because 45 = .75 * 60
at station B you get:
c - 25 = 60 - 25 = 35
a = 45 + 25 = 70
a = 70
c = 35
a = 2*c becomes 70 = 2*35 which becomes 70 = 70 which is true.
there were 100% more adults than children means that the number of adults is equal to the number of children plus another 100% of the children which is equal to 200% of the children which is equal to 2 times the number of children.
the numbers must be good.
a = 45
c = 60
your solution is:
70 adults were on the train when it left station B.
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