Error in Math Problem in Study Guide

[kquick0512]

I was reviewing the study guide in the above stickies and I just can't get over this one. Either I'm having a huge brain fart or it's wrong.

The one where it says a lady spends 1/5 of her income on rent, then 3/8 of the remainder income goes towards salary. It says final answer is 3/10 but that'd be wrong. If you take 1/5 out of 100 you get 80. Then 3/8 of 80 would be 30, thus leaving you with 50 or 5/8 of the remaining income or 1/2 of the overall income.

Is it the wording I'm getting stuck on? I'd assume that 3/8 of the remainder goes towards salary implies you're taking away 3/8 of the remaining 4/5 correct? Doesn't really make sense to put income into salary though?

I'm sure I'm just overthinking this one but can anyone explain?

 

[Tasha]

Hello,
We are given a number that she ends up with or begins with. Just that she spends 1/5 of her income on rent and 3/8 goes towards her salary. We can't assume it is out of 100.. and 1/5 of 100 is not 80, by the way.

In this case you're subtracting the amount of something from 1 to figure out your remaining.

1-(1/5) = (4/5) and from that (4/5) you multiply it by 3/8 and you get (3/10)

In this case there is (4/5) of her money is left and (3/8) isn't being taken away but rather given back and put towards her salary.. so you multiply to get your final answer.

Hope that helps.. I know its confusing because TOTAL AMT - X are very popular word problems. Just read the

 

[KilroyUSN]

It sounds like this question is asking, how much of her total income is going toward paying salary? So your "30" that you came up with, out of the "100" is the 3/10 that the answer is giving you.

For the record, he never said 1/5 of 100 is 80. He said "take 1/5 out of 100" which is what you did by saying "1-(1/5)". I don't have the question in front of me, but it sounds like he got confused as to what the question is looking for. He found how much money was left after subtracting rent and salary, instead of finding how much of the total income went to salary.

 

[Tycho_Brohe]

^^What he said. The wording is confusing, is she paying salary to someone else, or is the 3/8 of her remaining income comprised of her salary (and she has some other source of income that makes up the rest of it)? Seeing the actual question here might help.

 

[Tycho_Brohe]

In this case there is (4/5) of her money is left and (3/8) isn't being taken away but rather given back and put towards her salary.. so you multiply to get your final answer.

Right answer, wrong reasoning. Multiplying by a fraction will always give you a smaller number (except for improper fractions), so you would have to add the fractions if it was being added back in.

 

[Tasha]

It sounds like this question is asking, how much of her total income is going toward paying salary? So your "30" that you came up with, out of the "100" is the 3/10 that the answer is giving you.

For the record, he never said 1/5 of 100 is 80. He said "take 1/5 out of 100" which is what you did by saying "1-(1/5)". I don't have the question in front of me, but it sounds like he got confused as to what the question is looking for. He found how much money was left after subtracting rent and salary, instead of finding how much of the total income went to salary.

Oops! sorry for the misinterpretation. I thought he said 1/5 of 100! but yes, if you do take 1/5 out of 100 it is what I stated.

The question is: "A business woman spends 1/5 of her income on rent and 3/8 f the remainder goes towards salary. How much does she have remaining?"

Right answer, wrong reasoning. Multiplying by a fraction will always give you a smaller number (except for improper fractions), so you would have to add the fractions if it was being added back in.

I realized I worded that incorrectly as well which implies being added.. I had a hard time explaining why you multiply the 3/8.

 

[Tasha]

Oops! sorry for the misinterpretation. I thought he said 1/5 of 100! but yes, if you do take 1/5 out of 100 it is what I stated.

Oops- i meant to add, it is what I stated 1-(1/5) haha I don't know why I can't complete my sentences this morning. I need my coffee.

 

[Tycho_Brohe]

The question is: "A business woman spends 1/5 of her income on rent and 3/8 of the remainder goes towards salary. How much does she have remaining?"

Yeah, that's worded very poorly. I don't know what they were thinking when they wrote that. I would've done exactly what OP did in that case. Maybe if they asked "How much is the salary" or something like that. They're not really setting you up for success there.

 

[kquick0512]

Yea thanks for all the input. I'm guessing they're saying it from a fixed subtracted value from her original salary? Such as ins or taxes, so she'd be dropping 20 from the hypothetical "100" original salary, then has 3/8 of that remainder (80) to go towards her actual salary.

Weird wording was just trying to get it straightened out thank you everyone!

 

[Tasha]

Yeah, that's worded very poorly. I don't know what they were thinking when they wrote that. I would've done exactly what OP did in that case. Maybe if they asked "How much is the salary" or something like that. They're not really setting you up for success there.

I definitely have to agree with you .. a lot of study material is worded pretty poorly in the math sections! It always helps to do some outside research and use other sources! to verify. :O

 

[Tycho_Brohe]

Yea thanks for all the input. I'm guessing they're saying it from a fixed subtracted value from her original salary? Such as ins or taxes, so she'd be dropping 20 from the hypothetical "100" original salary, then has 3/8 of that remainder (80) to go towards her actual salary.

That might make sense, assuming it's talking about renting an office space. It still could have been worded better, because it still seems like it's asking about what's left over, not the salary itself.

 

[KilroyUSN]

Yea... I would agree, with the wording of the question, the answer should be 1/2.

The remainder after rent (4/5) + the remaining amount after salary (4/5 - 4/5 x 3/8) simplified to [8/10 - 3/10] , or "How much is remaining", would be 1/2.

Just realize you won't have to deal with shoddy mathematical questions in flight school.... poor questions trying to trick you in general however, are to be expected.