My Math Forum  

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

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


Thanks Tree6Thanks
  • 1 Post By v8archie
  • 1 Post By skipjack
  • 1 Post By skipjack
  • 1 Post By v8archie
  • 2 Post By skipjack
Reply
 
LinkBack Thread Tools Display Modes
October 7th, 2018, 04:25 PM   #1
Newbie
 
Joined: Sep 2018
From: Japan

Posts: 27
Thanks: 2

Ratio of pens and pencils

The ratio of the number of pens to the number of pencils in a box was 7:5. After 21 pens and 21 pencils were sold, the ratio became 11:7. How many pencils were left at the stall?

My work:

Ratio (before)
Pens:Pencils
7:5

Ratio (after)
Pens:Pencils
11:7

Since the ratio of both pens and pencils were sold, I twice the ratio for pens and pencils for before. Below is what I did

Ratio (before)
Pens:Pencils
7:5 * 2 =>

Pens:Pencils
14:10

Then I subtracted 14 - 11 (the 11 is the after ratio) and 10 - 7 (the 7 is the after ratio) and got 3 units

Since we know the difference for pens and pens is 21, below is what I did.

3 units = 21 => 1unit = 7.

How many pencils were left at the stall?

7 * 7 = 49 pencils were left.

Is my work correct?
xoritos is offline  
 
October 7th, 2018, 05:21 PM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,445
Thanks: 2499

Math Focus: Mainly analysis and algebra
\begin{align}
\text{Pens at end} &= p \\
\text{Pencils at end} &= q \\[12pt]
\text{after:} \; \frac p q &= \frac{11}7 \\
\text{before:} \; \frac{p+21}{q+21} &= \frac75
\end{align}
That's two equations in two variables that you can solve by your favourite method.

Your answer is correct. I don't recognise the method, but it seemed to work.
Thanks from xoritos

Last edited by v8archie; October 7th, 2018 at 05:50 PM.
v8archie is offline  
October 7th, 2018, 05:46 PM   #3
Global Moderator
 
Joined: Dec 2006

Posts: 19,713
Thanks: 1806

Quote:
Originally Posted by xoritos View Post
Is my work correct?
Your method and working were correct, but your explanation of why you did your first step of your solution doesn't make sense.
Thanks from xoritos
skipjack is offline  
October 7th, 2018, 07:32 PM   #4
Newbie
 
Joined: Sep 2018
From: Japan

Posts: 27
Thanks: 2

Quote:
Originally Posted by skipjack View Post
Your method and working were correct, but your explanation of why you did your first step of your solution doesn't make sense.
is this the one you are talking about?
------------------------------------------------
Since the ratio of both pens and pencils were sold, I twice the ratio for pens and pencils for before. Below is what I did

Ratio (before)
Pens:Pencils
7:5 * 2 =>

Pens:Pencils
14:10

----------------------------------------------

This is the part where I wasn't sure if it's mathematically correct, or what I explained was mathematically correct. What I did was since both ratios of pens and pencils changed. Since there is not equivalent ratio, I multiplied both the pens and pencils ratio by 2 so I can subtract the after ratio (11:7) from the modified before ratio (14:10) to get my single unit.


From what I understand with these ratio problems and using units to get an answer. The unit that doesn't change is fixed.


Quote:
Originally Posted by v8archie View Post
\begin{align}
\text{Pens at end} &= p \\
\text{Pencils at end} &= q \\[12pt]
\text{after:} \; \frac p q &= \frac{11}7 \\
\text{before:} \; \frac{p+21}{q+21} &= \frac75
\end{align}
v8archie, Thank you for this
xoritos is offline  
October 8th, 2018, 02:23 AM   #5
Global Moderator
 
Joined: Dec 2006

Posts: 19,713
Thanks: 1806

Quote:
Originally Posted by xoritos View Post
. . . Since there is not equivalent ratio, I multiplied both the pens and pencils ratio by 2 so I can . . .
The method is valid and your working was correct, but your justification for multiplying by 2 was "there is not equivalent ratio", which doesn't clearly explain why you chose to multiply by 2 rather than by some other number.
Thanks from xoritos
skipjack is offline  
October 8th, 2018, 04:47 AM   #6
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,445
Thanks: 2499

Math Focus: Mainly analysis and algebra
There's clearly some language barrier here, but my Japanese is non-existent. I think I now understand your idea, and it seems to be fine.
Thanks from xoritos
v8archie is offline  
October 9th, 2018, 04:07 PM   #7
Newbie
 
Joined: Sep 2018
From: Japan

Posts: 27
Thanks: 2

Quote:
Originally Posted by skipjack View Post
The method is valid and your working was correct, but your justification for multiplying by 2 was "there is not equivalent ratio", which doesn't clearly explain why you chose to multiply by 2 rather than by some other number.
You do have a good point. If I multiplied by 3, I would get a before ratio of (21:15). Then If I subtracted from the after ratio, I would get 21 - 11 = 10 units and 15 - 7 = 8 units. Which wouldn't work when dividing with 21. The way how I did it seems to work, but I'm not fully sure why.




Quote:
Originally Posted by v8archie View Post
There's clearly some language barrier here, but my Japanese is non-existent. I think I now understand your idea, and it seems to be fine.
Hehe
xoritos is offline  
October 9th, 2018, 04:13 PM   #8
Global Moderator
 
Joined: Dec 2006

Posts: 19,713
Thanks: 1806

The correct multiplier is (11 - 7)/(7 - 5) = 4/2 = 2.
Thanks from v8archie and xoritos
skipjack is offline  
October 9th, 2018, 05:25 PM   #9
Newbie
 
Joined: Sep 2018
From: Japan

Posts: 27
Thanks: 2

Quote:
Originally Posted by skipjack View Post
The correct multiplier is (11 - 7)/(7 - 5) = 4/2 = 2.
Thank you for this. That made it more sense
xoritos is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
pencils, pens, ratio



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Ratios: Pencils and Notebooks sigma Algebra 2 October 5th, 2018 02:01 AM
Find the dimensions of the rectangular corral split into two pens ................... GIjoefan1976 Algebra 2 December 7th, 2017 02:43 PM
ratio sunnyarain Elementary Math 6 October 19th, 2015 04:32 PM
About ratio satimis Applied Math 4 July 28th, 2009 04:16 PM





Copyright © 2018 My Math Forum. All rights reserved.