Checking Spending Habits: How Much for Health Care?

[tionis]

Hi, guys. Would you please check if my homework is correct. The graph below shows how the average consumer spends money:

Education-------- 1_/50

Insurance-------- 1_/10

Entertainment---1_/25

Health care----- -3_/50

Transportation---1_/5

Clothing-----------1_/25

Housing----------- 8_/25

Food--------------- 7_/50

Other-------------- 2_/25

Q: What fraction of spending goes for housing and food?

My answer is 23_/50.

Q: What fraction of spending goes for education, transportation, and clothing?

My answer is 13_/50.

Q: Suppose your family spent $47,000 on the items in the graph. How much might we expect was spent on health care?

I'm having trouble with this one. OK, so I think I should subtract 8_/50 from 47000, right?

47,000_/1 - 8_/50 = 2350000_/50 - 8_/50 = 2349992_/50 = 2349992 ÷ 50 = 46999.84? That can't be right. What am I doing wrong? I think my first two answers are correct, but this last one stumped me, so I've lost confidence. Please help. Thank you.

 

[Borg]

Q: Suppose your family spent $47,000 on the items in the graph. How much might we expect was spent on health care?

I'm having trouble with this one. OK, so I think I should subtract 8/50 from 47000, right?

47,000/1 - 8/50 = 2350000/50 - 8/50 = 2349992/50 = 2349992 ÷ 50 = 46999.84? That can't be right. What am I doing wrong? I think my first two answers are correct, but this last one stumped me, so I've lost confidence. Please help. Thank you.

Think about it this way - if someone asked you what half of $47,000 was, you would know right away. The only difference is that the problem is dealing with 8/50 instead of 1/2.

 

[tionis]

Think about it this way - if someone asked you what half of $47,000 was, you would know right away. The only difference is that the problem is dealing with 8/50 instead of 1/2.

I just don't get it, Borg. Are my steps wrong? So I have 47000 and 8/50, right? Then I turn 47000 into an improper fraction --> 47000/1. I now have 47000/1 which I have to convert to 47000/50 so that both denominators match in order for me to subtract. When I do that, I multiply 50 x the numerator 47000. That yields --> 2,350,000/50! from which I now subtract 8, thus getting 2,349,992. Even when I simplify 2,349,992 and 50 to 11174996/25 and divide, I get 46999.84.

 

[Borg]

Go back to my original answer. If someone asked you what 1/2 of 47000 was, would you subtract 0.5 from 47000?

 

[tionis]

Go back to my original answer. If someone asked you what 1/2 of 47000 was, would you subtract 0.5 from 47000?

OK, I see what you're saying lol. No, I wouldn't. So what should I do? Should I turn 8/50 into 8000/50?

 

[Borg]

OK, I see what you're saying lol. No, I wouldn't. So what should I do? Should I turn 8/50 into 8000/50?

Would you do that for the 1/2? No. So why would you do it for the 8/50 fraction? You're really overthinking the answer. Just substitute 8/50 in place of the 1/2.

 

[tionis]

Would you do that for the 1/2? No. So why would you do it for the 8/50 fraction? You're really overthinking the answer. Just substitute 8/50 in place of the 1/2.

Oh! I have to divide 47000 ÷ 8/50? But that yields 293750/1. Is this correct?

 

[Borg]

Multiply, not divide.

 

[Ray Vickson]

Oh! I have to divide 47000 ÷ 8/50? But that yields 293750/1. Is this correct?

Why would you want to divide? Would 1/2 of 5000 equal 5000/(1/2) = 10000?

 

[tionis]

Multiply, not divide.

OK, when I multiply, I get 7520/1. Is this correct?

Why would you want to divide? Would 1/2 of 5000 equal 5000/(1/2) = 10000?

lol I really don't have any clue.

 

[Borg]

OK, when I multiply, I get 7520/1. Is this correct?

It makes a lot more sense than the previous attempts.

 

[SteamKing]

Why would you want to divide? Would 1/2 of 5000 equal 5000/(1/2) = 10000?

lol I really don't have any clue.

You mean you don't know what half of 5000 is?

IMO, you're starting too advanced. You need to review basic arithmetic, like adding, subtracting, multiplying, and dividing.

 

[Mark44]

I just don't get it, Borg. Are my steps wrong? So I have 47000 and 8/50, right? Then I turn 47000 into an improper fraction --> 47000/1. I now have 47000/1 which I have to convert to 47000/50

No. These two numbers are not equal

Should I turn 8/50 into 8000/50?

No again. $\frac {8}{50} \ne \frac {8000}{50}$.
When you work toward a common denominator, what you should get are two fractions that are equal. For example, $\frac 2 3$ and $\frac 8 {12}$ are different representations of the same number. $\frac{8}{50}$ and $\frac{8000}{50}$ are not the same.
In any case, subtraction of fractions (and common denominators) are completely irrelevant in this problem.

Oh! I have to divide 47000 ÷ 8/50? But that yields 293750/1. Is this correct?

No.

IMO, you're starting too advanced. You need to review basic arithmetic, like adding, subtracting, multiplying, and dividing.

In particular, how to add, subtract, multiply, and divide fractions.

You said in another thread that you plan to study physics in college next year. If you don't get a handle on doing pretty basic arithmetic, you won't get very far in physics.

 

[tionis]

It makes a lot more sense than the previous attempts.

OK, I think I finally got it So, I multiply 47000 x 8 = 141000, then divide it by 50 = 2820? I hope so 'cause I don't know what else to do lol.

You mean you don't know what half of 5000 is?IMO, you're starting too advanced. You need to review basic arithmetic, like adding, subtracting, multiplying, and dividing.

Half of 5000 is 2500.

If you don't get a handle on doing pretty basic arithmetic, you won't get very far in physics.

Very true, but I'm in no rush.

 

[Borg]

OK, when I multiply, I get 7520/1. Is this correct?

OK, I think I finally got it So, I multiply 47000 x 8 = 141000, then divide it by 50 = 2820?

Are you even paying attention to your own answers from one post to the next?

 

[jbriggs444]

I multiply 47000 x 8 = 141000, then divide it by 50 = 2820?

To multiply an integer (e.g. 47000) by a fraction (e.g. $\frac{8}{50}$, you multiply by the numerator and then divide by the denominator, yes. So that part is correct.

But 47000 multiplied by 3 gives 141000. You were supposed to be multiplying by 8.

You should get into the habit of checking your work. One way of doing this is with estimation. Eight is nearly ten. Multiplying 47 thousand by 8 should give you something a bit less than 470 thousand. A result of 141 thousand is way too low.

Or you could notice that 47 is close to 50. So 47 thousand times $\frac{8}{50}$ should be close to 8 thousand. But 2820 is not close to 8 thousand.

Another sanity check could be to notice that you multiplied an odd number (47) by an even number (8) and got an odd number (141) as a result.

 

[tionis]

Are you even paying attention to your own answers from one post to the next?

I'm sorry, Borg Thank you for your help.

To multiply an integer (e.g. 47000) by a fraction (e.g. $\frac{8}{50}$, you multiply by the numerator and then divide by the denominator, yes. So that part is correct..

Yes! And just in time. Thank you, jbriggs444.