Help to create an Algebraic equation

matrixebiz

New member
Joined
Jan 14, 2015
Messages
13
Hello, I'm hoping someone can help me create an equation out of the below word problem.
-------------------------------------------------------------------------------------------------------------------------------------
A couple living together have a combined bill payment of $1600.
Jane makes a wage of $2900 a month and John makes a wage of $2000 a month.
To make it fair John should pay a bit less percentage of his wage (being the lesser income maker) towards the bill so they have an equal amount percentage of income at the end of the month left over.
Based on their income ratio, what percentage of their monthly income should they pay towards the bill?
-------------------------------------------------------------------------------------------------------------------------------------

Doing some simple math, it would be fair to say that they each should pay approximately 33% of ones income a month which will leave each 66% in pocket.
But I'm looking to get this into a formula so that if any of the values change IE: Wage or Bill amount or Both, I can then quickly work out the percentage they each need to pay to make it fair based on separate/different income amount. Thank you
 
Hello, I'm hoping someone can help me create an equation out of the below word problem.
-------------------------------------------------------------------------------------------------------------------------------------
A couple living together have a combined bill payment of $1600.
Jane makes a wage of $2900 a month and John makes a wage of $2000 a month.
To make it fair John should pay a bit less percentage of his wage (being the lesser income maker) towards the bill so they have an equal amount percentage of income at the end of the month left over.
Based on their income ratio, what percentage of their monthly income should they pay towards the bill?
-------------------------------------------------------------------------------------------------------------------------------------

Doing some simple math, it would be fair to say that they each should pay approximately 33% of ones income a month which will leave each 66% in pocket.
But I'm looking to get this into a formula so that if any of the values change IE: Wage or Bill amount or Both, I can then quickly work out the percentage they each need to pay to make it fair based on separate/different income amount. Thank you
Start by naming things you want to find: Call the amount Jane pays each month "x" and the amount John pays "y".
The combined bill is $1600 so x+ y= 1600. Jane will have $2900- x left over so the fraction of her income left over will be \(\displaystyle \frac{2900- x}{2900}\). John will have $2000- y left over so the fraction of his income left over will be \(\displaystyle \frac{2000- y}{2000}\). In order that they pay the same percentage of income left over we must have \(\displaystyle \frac{2900- x}{2900}= \frac{2000- y}{2000}\).

You need to solve the simultaneous equations \(\displaystyle x+ y= 1600\) and \(\displaystyle \frac{2900- x}{2900}= \frac{2000- y}{2000}\).
 
Start by naming things you want to find: Call the amount Jane pays each month "x" and the amount John pays "y".
The combined bill is $1600 so x+ y= 1600. Jane will have $2900- x left over so the fraction of her income left over will be \(\displaystyle \frac{2900- x}{2900}\). John will have $2000- y left over so the fraction of his income left over will be \(\displaystyle \frac{2000- y}{2000}\). In order that they pay the same percentage of income left over we must have \(\displaystyle \frac{2900- x}{2900}= \frac{2000- y}{2000}\).

You need to solve the simultaneous equations \(\displaystyle x+ y= 1600\) and \(\displaystyle \frac{2900- x}{2900}= \frac{2000- y}{2000}\).

Ok, thx but I must not be understanding something because when I solve that, it is;

x + y = 1600 and -1x = -1y

Where does that leave me?
 
Last edited:
Surely you see that "-1x= -1y" is the same as x= y? And since y is equal to x, we can replace y with x: x+ y= x+ x= 2x= 1600.
 
Ok, thx but I must not be understanding something because when I solve that, it is;

x + y = 1600 and -1x = -1y

Where does that leave me?
I am not sure where you get -1x=-1y but that means that x=y and so x=y=$800. But that is not correct. If you tell us how you got -1x=-1y we can explain where you went wrong.

Although the method already described about is a very good method I did it slightly differently.

x+y = 1600 and x/2900 = y/2000. x/2900 is the part of Jane's income that is going towards paying the bill and y/2000 is the part of John's income that is going towards paying the bill. We want these parts to be equal.

Using the these two equations you can solve for x and y
 
Ok, thank you for the suggestions.

I think his should work too;

Since they should each pay a percentage of their combined income required to cover the bill

in this case

1600/(2900+2000) = 0.3265306122449

so each should pay 32.6%
 
Ok, thank you for the suggestions.

I think his should work too;

Since they should each pay a percentage of their combined income required to cover the bill

in this case

1600/(2900+2000) = 0.3265306122449

so each should pay 32.6%
Well if you want to round off to 1 decimal place it should be 32.7% as the digit to the right of 6 is a 5.
I like the way you are doing it! Can you show us your final result please?
 
Well if you want to round off to 1 decimal place it should be 32.7% as the digit to the right of 6 is a 5.
I like the way you are doing it! Can you show us your final result please?

Hi Jomo,

So John will need to pay $653 (32.65% of $2000) and Jane will need to pay $947 (32.65% of $2900) to cover the $1600 bill


They both retain 67.35% of their income each
 
I think his should work too;

Since they should each pay a percentage of their combined income required to cover the bill

in this case

1600/(2900+2000) = 0.3265306122449

so each should pay 32.6%
Yes, quoting another tutor, word for word, is likely to produce a valid result. But what have you done on this? What efforts have you invested? Do you understand what is going on? ;)
 
Hi Jomo,

So John will need to pay $653 (32.65% of $2000) and Jane will need to pay $947 (32.65% of $2900) to cover the $1600 bill


They both retain 67.35% of their income each
I got 653.06 and 946.94 but with round off errors you are correct. Great job! Now do some more problems!
 
Yes, quoting another tutor, word for word, is likely to produce a valid result. But what have you done on this? What efforts have you invested? Do you understand what is going on? ;)
I haven't done anything except post his answer to provide another viable solution along with the other ones posted here. Sorry I didn't put it in Quotes.
Posting links to other forums is banned by mods at other places/forums I've been on.
 
Last edited:
Last edited:

I am a member of many different types of forums which have rules like this so I think there was just some confusion, I would agree that it would be fair that Math/Tutor specific forums be allowed to help one another in finding a final solution together. I didn't think that Denis was strictly referring to Math/Tutor type forums so I misinterpreted his statement and Stapel to mine, as I didn't want to brake any rules. Clearly I didn't read this forum rules about sharing (my bad) and was solely relying on my past experience with other different types of forum rules. It's all good now.
 
Last edited:
Top