7th grade math problem

[ElizK]

Ok, this silly thing is driving me nuts. DD12 had the following problem yesterday on a math worksheet:

A can (of whatever) weighs 10 1/2 oz and cost 98 cents. How much does one ounce cost?

I know the answer (because of the worksheet... it would take too long to explain), but I can't figure out how to get there. The math whiz that I work with came up with the same answer I did, but it's wrong! I know it's that stupid 1/2 oz that's throwing off the answer. HELP!

 

[chris1gill]

It's .98 divided by 10.5 with an answer of 9.3333 repeating if I'm not mistaken....

 

[RobInBigKC]

Ok, this silly thing is driving me nuts. DD12 had the following problem yesterday on a math worksheet:

A can (of whatever) weighs 10 1/2 oz and cost 98 cents. How much does one ounce cost?

I know the answer (because of the worksheet... it would take too long to explain), but I can't figure out how to get there. The math whiz that I work with came up with the same answer I did, but it's wrong! I know it's that stupid 1/2 oz that's throwing off the answer. HELP!

Is this a trick question? Wouldn't it just be 98 cents divided by 10.5 ounces gives you 9.3333333 cents per ounce?

What wrong answer are you getting? What is the correct answer?

-- Rob

 

[hlbtimes2]

.98 divided by 10.5 is .0933 per ounce. If you mulitiple it back out .0933 x 10.5 you get .97965

edit: looks like most of us came up with the same or close answer. What wrong answer did you have?

 

[ElizK]

Ok, I was dividing 10.5 by .98, so I was doing that much backwards. But, the correct answer is 8.5 cents per oz, according to the worksheet.

 

[agnes!]

Ok, this is how I figured it out. Might be wrong, but here goes...

Take .98.
Divide by the number of 1/2 ounces, that would be 21.
That answer is .0466.
That's how much 1/2 ounce costs.
Double the .0466 which equals .0932.
That's how much 1 ounce costs.

I think...

agnes!

 

[RobInBigKC]

Ok, I was dividing 10.5 by .98, so I was doing that much backwards. But, the correct answer is 8.5 cents per oz, according to the worksheet.

Wow! I honestly think your worksheet is wrong.

8.5 cents per ounce multiplied by the 10.5 ounces would make the total cost $.89. It is possible the 8 and 9 in 89 were mistyped to make 98?

-- Rob

 

[Buckalew11]

Wow! I honestly think your worksheet is wrong.

8.5 cents per ounce multiplied by the 10.5 ounces would make the total cost $.89. It is possible the 8 and 9 in 89 were mistyped to make 98?

-- Rob

Either that or the teacher had a coupon she forgot to tell about.

 

[agnes!]

Ok, I was dividing 10.5 by .98, so I was doing that much backwards. But, the correct answer is 8.5 cents per oz, according to the worksheet.

But when I multiply the number of ounces (10.5) by the supposed cost per ounce($.085), I'm coming up with 89 cents for the can...

agnes!

 

[ElizK]

Wow! I honestly think your worksheet is wrong.

8.5 cents per ounce multiplied by the 10.5 ounces would make the total cost $.89. It is possible the 8 and 9 in 89 were mistyped to make 98?

-- Rob

I suppose it is possible. I may have to email the teacher. I have this math obsession. MUST. FIGURE. OUT. PROBLEM.


Thanks, everyone, for your help.

 

[agnes!]

I agree with the other posters - Worksheet is wrong.

If you multiply 10.5(ounces)x.093(cost per ounce) you get .9765 which rounds up to 98 cents.

agnes!

 

[CPM]

It does happen sometimes. My DH has pointed out several mistakes on our son's worksheets.

 

[RobInBigKC]

It does happen sometimes. My DH has pointed out several mistakes on our son's worksheets.

UGH! Here too. Makes it MUCH harder to solve problems.

-- Rob

 

["Got Disney"]

 

[RobInBigKC]

[QUOTE="Got Disney";21151285]I got 10.7 per ounce .....10.5 divided by .98 did you forget to put the decimal point infront of the 98 for 98 cents ?[/QUOTE]
Cost ($.98) divided by size (10.5 ounces) gives you cost per unit of measurement (ounce, in this case). $.98 / 10.5 = $.0933333333 or 9.33333 cents per ounce.

-- Rob

 

[Kathi OD]

The correct way to solve the problem is to change the 98 cents to a decimal - .98 and then divide by 10.5. The answer is .093 or 9 and 1/3 cents. Either the worksheet answer is wrong or the problem was typed incorrectly.

 

["Got Disney"]

Cost ($.98) divided by size (10.5 ounces) gives you cost per unit of measurement (ounce, in this case). $.98 / 10.5 = $.0933333333 or 9.33333 cents per ounce.

-- Rob

Ahhhh yes but also 10.7 X .98 = 10.486 almost 10.5....... 9.3 X ,98 = 9.114

So if you plug back in the 9.3 it is farther off to estmate your answer.

 

[RobInBigKC]

[QUOTE="Got Disney";21151367]Ahhhh yes but also 10.7 X .98 = 10.486 almost 10.5....... 9.3 X ,98 = 9.114

So if you plug back in the 9.3 it is farther off to estmate your answer.[/QUOTE]

Why would you multiply your cost per ounce figure (10.7 cents per ounce) times the price of the can ($.98) to get the size of the can? Cost of the size unit times total price does not give you size. Total price divided by cost of the size unit would be the formula to get the size of the purchase.

To check your answer you would multiply price per ounce ($.0933333 in my answer) times the number of ounces in the can (10.5) (NOT the price of the can) to get the cost of the can ($.093333333 x 10.5 = $.97999999999999999 or 98 cents).

OR you can check it by taking the total price ($.98) divided by the price per ounce that was figured ($.09333333333 in my case) to get the size of the purchase ($.98 / $.09333333333333 = 10.5, i.e. 10.5 ounces).

-- Rob

 

["Got Disney"]

Why would you multiply your cost per ounce figure (10.7 cents per ounce) times the price of the can ($.98) to get the size of the can? Cost of the size unit times total price does not give you size. Total price divided by cost of the size unit would be the formula to get the size of the purchase.

To check your answer you would multiply price per ounce ($.0933333 in my answer) times the number of ounces in the can (10.5) (NOT the price of the can) to get the cost of the can ($.093333333 x 10.5 = $.97999999999999999 or 98 cents).

OR you can check it by taking the total price ($.98) divided by the price per ounce that was figured ($.09333333333 in my case) to get the size of the purchase ($.98 / $.09333333333333 = 10.5, i.e. 10.5 ounces)

-- Rob

the question is asking how much each oz. cost in the can. not the size of the can.
And when you divide to check your answer you multipy.

so if there are 10.5 oz in the can and all the oz together cost .98 cents than you would have 10.5 divided by .98 cents = 10.7

!0.5 = wt of all the ounces x .98 the price of each ounce.

I just checked with my straight A gate math student, 8th grade and he came up with the same answer as me. He said that you are whats called repeating and he said you are dividing the 10.5 into the 98 you are suppose to be dividing the .98 into the 10.5

O well who cares ...who ever invented word problems anyway

We are both tired and can both be wrong tonigt... he is watching TV at the same time I asked him and he figured it out in his head .... he is in Geometry in the 8th grade ...passed Algebra one in 7th ....I am curious though so I will ask his teacher tomorrow and ask also how the answer is 89 or what ever it is.

 

[RobInBigKC]

the question is asking how much each oz. cost in the can. not the size of the can.
And when you divide to check your answer you multipy.

so if there are 10.5 oz in the can and all the oz together cost .98 cents than you would have 10.5 divided by .98 cents = 10.7

10.5 = wt of all the ounces x .98 the price of each ounce.

I just checked with my straight A gate math student, 8th grade and he came up with the same answer as me. He said that you are whats called repeating and he said you are dividing the 10.5 into the 98 you are suppose to be dividing the .98 into the 10.5

Ok, I wrote all this before I saw the edit of your last post so I will go ahead and post it as the "proof for my theorem ".

True.
Also true.

Ok, we agree that the total cost of the can is $.98. We agree that the total size of the can is 10.5 ounces. We agree that the question is cost per ounce.

Let me try this one more time, long-hand this time... first with your answer:
Ounce 1 costs 10.7 cents so a 1 ounce can costs 10.7 cents.
Another ounce also costs 10.7 cents so a 2 ounce can costs 10.7 + 10.7 or 21.4 cents.
Another ounce also costs 10.7 cents so a 3 ounce can costs 21.4 + 10.7 or 32.1 cents.
Another ounce also costs 10.7 cents so a 4 ounce can costs 32.1 + 10.7 or 42.8 cents.
Another ounce also costs 10.7 cents so a 5 ounce can costs 42.8 + 10.7 or 53.5 cents.
Another ounce also costs 10.7 cents so a 6 ounce can costs 53.5 + 10.7 or 64.2 cents.
Another ounce also costs 10.7 cents so a 7 ounce can costs 64.2 + 10.7 or 74.9 cents.
Another ounce also costs 10.7 cents so a 8 ounce can costs 74.9 + 10.7 or 85.6 cents.
Another ounce also costs 10.7 cents so a 9 ounce can costs 85.6 + 10.7 or 96.3 cents.
Another ounce also costs 10.7 cents so a 10 ounce can costs 96.3 + 10.7 or 107 cents.
Another 1/2 ounce costs 1/2 of 10.7 cents (or 5.35 cents) so a 10.5 ounce can costs 107 + 5.35 or 112.35 cents.
Now, 112.35 cents is obviously greater than 98 cents.

Ok, let's try the long way with my answer: (I assume you understand that 9.3333 cents per ounce is actually 9.33 and a third cents per ounce.)
Ounce 1 costs 9.3333 cents so a 1 ounce can costs 9.3333 cents.
Another ounce also costs 9.3333 cents so a 2 ounce can costs 9.3333 + 9.3333 or 18.6666 cents.
Another ounce also costs 9.3333 cents so a 3 ounce can costs 18.6666 + 9.3333 or 28 cents.
Another ounce also costs 9.3333 cents so a 4 ounce can costs or 28 + 9.3333 or 37.3333 cents.
Another ounce also costs 9.3333 cents so a 5 ounce can costs 37.3333 + 9.3333 or 46.6666 cents.
Another ounce also costs 9.3333 cents so a 6 ounce can costs 46.6666 + 9.3333 or 56 cents.
Another ounce also costs 9.3333 cents so a 7 ounce can costs 56 + 9.3333 or 65.3333 cents.
Another ounce also costs 9.3333 cents so a 8 ounce can costs 65.3333 + 9.3333 or 74.6666 cents.
Another ounce also costs 9.3333 cents so a 9 ounce can costs 74.6666 + 9.3333 or 84 cents.
Another ounce also costs 9.3333 cents so a 10 ounce can costs 84 + 9.3333 or 93.3333 cents.
Another 1/2 ounce costs 1/2 of 9.3333 cents (or 4.6666 cents) so a 10.5 ounce can costs 93.3333 + 4.6666 or 98 cents.

----------------------------
Responding to your edit: Ok, please have him check. He can print this whole thread and take it to school to see what they all think.

Just wait until he gets into Quantitative Analysis -- it's nothing BUT super, super complex word problems!

-- Rob