
By: Tping (offline) Monday, March 25 2013 @ 07:23 PM CDT (Read 696 times)



Tping 
Hi, please help..
At Station A, the ratio of the number of children to the number of adults on a train was 4:5.
At the next station, 12 children alighted and 10 adults boarded the train.
The ratio of the number of children to the number of adults on the train then became 7:10.
How many children were on the train at first?
Thank you.

Junior
Registered: 01/26/12 Posts: 25





By: echeewh (offline) Tuesday, March 26 2013 @ 03:28 AM CDT



echeewh 
Hey Tping,
This is a typical <Changed Qtys> question in which any of Model method, CrossMultiply method or Simultaneous (Parts & Units) method can be used.
Following pls find my worked solution:
Given that both <Before> and <After> ratios and <Changed Qtys> are given, we can use the CrossMultiply method as shown:
<Before>
C : A
4 : 5
<Process>
C: 12
A: +10
<After>
C : A
7 : 10
(4u  12) / 7 = (5u + 10) / 10
10 × (4u  12) = 7 × (5u + 10)
40u  120 = 35u + 70
40u  35u > 120 + 70
5u > 190
1u > 38
Number of Children (C) (at first) = 4u > 4 × 38
= 152
==============
Trust this helps.
Do let me know again if this is different from your Answerkey or if there's further clarification.
Cheers,
Edward

Active Member
Registered: 04/21/11 Posts: 623



