FDP pg 91 qn 3

[SherryK835]

How do you solve this question without choosing a smart number? There has to be a way to solve the algebraic equations without plugging in a integer value for the monthly paychecks.

Question from book:
Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate, Carie, who earns twice as much as Lisa, spends 1/4 of her monthly paycheck on rent and 1/2 on food. If the two women decide to donate the remainder of their money to charity each month, what fraction of their combined monthly income will they donate?



This is where I got to so far:
PL and CL refer to Lisa's Paycheck and Charitable contibutions
PC and CC refer to Carrie's

PL=(19+CL)/24
PC=(3+CC)/4
PC=2PL

We need to find CL+CC

Total Income (TI) = PC + 2PL

I've tried many iterations at this point but keep getting lost.

Thanks for your help!

[tim]

Please note that the forum rules indicate you need to include the full text of the problem before we can discuss it, so that other students can benefit from the discussion as well.

[SherryK835]

Thank you Tim, I just edited my post and added the full question from the book.

My question was how to solve it algebraically without plugging in numbers.

[RonPurewal]

the problem asks for a fraction of the two women's combined income.

thus, if you want to use algebra, it's most sensible to define a variable for that combined income.
say 'x' = combined income

then, since carrie earns twice as much as lisa, carrie's income is 2x/3, and lisa's is x/3.
now take the appropriate fractions of these, and go from there.

[SherryK835]

Thank you Ron.

The answer in the book is 17/72. I tried with equating the combined income to x, and therefore Lisa as 1/3x and Carrie 2/3x. I am getting 14/72

Lisa Charity = 1/3 * [1-(3/8 + 5/12)] = 5/72
Carrie Charity = 2/3 * [1-(1/4+1/2)] = 1/6

1/6 + 5/72 = 14/72

Where am I making a mistake?

[RonPurewal]

1/6 is equal to 12/72. you seem to have converted it into 9/72 by mistake.

watch your arithmetic!

[SherryK835]

Thanks Ron. I'm embarrassed I made such a mistake.
Appreciate all your help on this one!

[RonPurewal]

i make arithmetic mistakes all the time. especially subtraction-- i'd say i make mistakes on somewhere between 10 and 20 percent of all subtraction operations i ever do.

the point here is just to be aware of the mistakes that YOU typically make.
this is just like any other form of self-awareness: you just have to know your own skill set—both strengths and weaknesses—which won't be the same as anyone else's.

[RonPurewal]

in fact, your skill set is likely to have VERY specific quirks, attributable to the particulars of your own background.
in my case, for instance, i can perform the following mental operations flawlessly:
* addition
* multiplication by 4, 5, 7, and 9
* division by 4, 5, and 7
in each case there are specific reasons. e.g., i've kept more than 10 years' worth of food diaries, which entail multiplying pretty much everything by 4 and 9 (= calories/gram of carb/protein and fat, respectively) and then adding the results. so that's the provenance of the 4's and 9's. the other numbers are schedule-related.

with any other operation, i have to double- and perhaps even triple-check.

of course the point is not 'ron has a really weird skill set'; the same is almost certainly true for anyone else who wrangles with numbers on a regular basis.
the point is 'ron knows where he NEEDS to be more or less careful'. this is a key component of efficiency: exercise extra diligence where extra diligence is actually necessary.


in my case, for instance, i know that i just have to double-check every time i do subtraction. (by contrast, after keeping food diaries for more than 10 years, i pretty much never make mistakes with mental addition, or with multiplication by 4 or 9.)

[SherryK835]

Excellent advice. Thank you. As I take the GMAT class and go through the homework, I have started to become more aware of what my weaknesses are with the GMAT and trying to spend more time reviewing/ practicing those types of questions.

[RonPurewal]

great!