My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Reply
 
LinkBack Thread Tools Display Modes
August 2nd, 2019, 10:05 AM   #1
Senior Member
 
Joined: Aug 2014
From: India

Posts: 476
Thanks: 1

Solve this two doubts in mixture problem.

A can contains a mixture of two liquids A & B in the ratio 7:5 When 9 liters of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. Liters of liquid A contained by the can intially was?

Solution: A:B Ratio 7:5
A:B = 7:9
4===9
16===36*7/12=21

How 4 corresponds to 9? Why 4 is multiplied both sides to get 16 & 36 in last step?
Ganesh Ujwal is offline  
 
August 2nd, 2019, 01:14 PM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 21,026
Thanks: 2257

The 7:5 ratio represents 7(9/4)L:5(9/4)L, which total 12(9/4)L. (The 9/4 comes from 9/(9 - 5).)
To get the original volumes, one scales up by (12(9/4) + 9)/(12(9/4)), which is 4/3.
Hence the original volume of A was 7(9/4)(4/3)L = 7(36/12)L = 21L.

The above explains everything except the "16" in the last line of the solution. I'm not sure why it's there.
skipjack is online now  
August 2nd, 2019, 08:09 PM   #3
Senior Member
 
Joined: Aug 2014
From: India

Posts: 476
Thanks: 1

Quote:
Originally Posted by skipjack View Post
The 7:5 ratio represents 7(9/4)L:5(9/4)L
How 9/4 came?
Ganesh Ujwal is offline  
August 3rd, 2019, 04:38 AM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 21,026
Thanks: 2257

The 9 is because 9L of liquid B are added. The 4 is because the A:B ratio changes from 7:5 to 7:9 and 9 - 5 = 4.

Multiplying both numbers in the ratio by 9/4 doesn't change the ratio, but changes the increase in the second value from 4 to 9. The numbers used for the ratio have therefore become the numbers of Liters of liquids A and B.
skipjack is online now  
August 4th, 2019, 03:16 AM   #5
Senior Member
 
Joined: Aug 2014
From: India

Posts: 476
Thanks: 1

Quote:
Originally Posted by skipjack View Post
The numbers used for the ratio have therefore become the numbers of Liters of liquids A and B.
How numbers in ratio become the number of liters of Liquids A & B?
Ganesh Ujwal is offline  
August 4th, 2019, 10:55 AM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 21,026
Thanks: 2257

The 7:5 ratio becomes written as (63/4):(45/4).
The 7:9 ratio becomes written as (63/4):(81/4).
Now 45/4 + 9 = 81/4, and clearly any factor other than 9/4 wouldn't achieve that.
Hence (63/4)L and (45/4)L are the volumes immediately prior to 9L of liquid B being added.
skipjack is online now  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
doubts, mixture, problem, solve



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Please solve my 2 doubts in this solution. Ganesh Ujwal Number Theory 3 May 3rd, 2018 03:26 AM
Mixture Problem Kimmysmiles0 Algebra 2 April 4th, 2012 07:38 PM
mixture problem weeweewee Algebra 1 January 6th, 2012 01:51 AM
Mixture Problem, please help Horizont Algebra 3 September 16th, 2008 10:12 AM





Copyright © 2019 My Math Forum. All rights reserved.