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

Algebra ->  Percentage-and-ratio-word-problems -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Instead of percents, use fractions
25% = +1%2F4+
100% = +1+
--------------
Let +a+ = number of adults on train
Let +c+ = number of children on train
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At station A:
(1) +a+=+c+-+%281%2F4%29%2Ac+
At station B:
+c+-+25+ children are left
+a+%2B+25+ adults on train
(2) +a+%2B+25+=+c+-+25+%2B+1%2A%28+c+-+25+%29+
-----------------------------------
(1) +4a+=+4c+-+c+
(1) +4a+=+3c+
(1) +c+=+%284%2F3%29%2Aa+
--------------------
(2) +a+%2B+25+=+2c+-+50+
(2) +a+=+2c+-+75+
By substitution:
(2) +a+=+2%2A%284%2F3%29%2Aa+-+75+
(2) +%28+8%2F3%29%2Aa+-+a+=+75+
(2) +%285%2F3%29%2Aa+=+75+
(2) +5a+=+225+
(2) +a+=+45+
----------------
When the train left station B, there were
+a+%2B+25+=+45+%2B+25+
+a+%2B+25+=+70+ adults on board
--------------------------------
check:
(1) +a+=+c+-+%281%2F4%29%2Ac+
(1) +45+=+c+-+%281%2F4%29%2Ac+
(1) +%283%2F4%29%2Ac+=+45+
(1) +c+=+%284%2F3%29%2A45+
(1) +c+=+60+
and
(2) +a+%2B+25+=+c+-+25+%2B+1%2A%28+c+-+25+%29+
(2) +45+%2B+25+=+c+-+25+%2B+1%2A%28+c+-+25+%29+
(2) +70+=+2c+-+50+
(2) +2c+=+120+
(2) +c+=+60+
OK

Answer by Theo(13342) About Me  (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.