Calculation Interpretation

[Explain this!]

Two cans of fruit can be purchased for $1.00. What is the cost of 12 cans?

$1.00/2 cans * 12 cans = $6.00

I interpret the above calculation as 6 groups of 2 cans at $1.00 per group of 2 cans. Is this correct?

Here is another situation similar to the one above.

If the finance charge is $20.00 on an amount financed of $400.00, what is the finance charge if the amount financed is $100.00?

My solution is as follows: $20.00/$400.00 * $100.00 = $5.00

Is the following interpretation for the above calculation correct: 1/4 group of $400.00 at 20 dollars per group of $400.00?

What is a better way to interpret or word the meaning of the calculation?

 

[lev888]

Two cans of fruit can be purchased for $1.00. What is the cost of 12 cans?

$1.00/2 cans * 12 cans = $6.00

I interpret the above calculation as 6 groups of 2 cans at $1.00 per group of 2 cans. Is this correct?

I don't think so.
$1.00/2 is the price of one can.
Result * 12 is the total price of 12 cans.

 

[Dr.Peterson]

Two cans of fruit can be purchased for $1.00. What is the cost of 12 cans?

$1.00/2 cans * 12 cans = $6.00

I interpret the above calculation as 6 groups of 2 cans at $1.00 per group of 2 cans. Is this correct?

I would say that your description is a different way to get the same result: The 12 cans can be considered to be 6 sets of 2, each of which costs $1, so that the total cost is $6.

But that is not an explanation of the meaning of the specific calculation you show. They have found the price of one can, and multiplied by 12 to get the price of 12.

If the finance charge is $20.00 on an amount financed of $400.00, what is the finance charge if the amount financed is $100.00?

My solution is as follows: $20.00/$400.00 * $100.00 = $5.00

Is the following interpretation for the above calculation correct: 1/4 group of $400.00 at 20 dollars per group of $400.00?

Again, you are describing two different calculations. The description you ask about does not describe the calculation you did, though both give the same correct result.

When you write "$20.00/$400.00 * $100.00 = $5.00", you are finding the charge per dollar financed, then applying that to find the charge for $100.

When you write "1/4 group of $400.00 at 20 dollars per group of $400.00", you would calculate that as $100/$400 = 1/4, and 1/4 * $20 = $5. Or you could express this as $20 * ($100/$400).

I would say that the first way is easier and clearer.

 

[Explain this!]

I don't think so.
$1.00/2 is the price of one can.
Result * 12 is the total price of 12 cans.

No, the price for 2 cans is $1.00. 12 cans would be 12/2 * $1.00 = $6.00

 

[Dr.Peterson]

No, the price for 2 cans is $1.00. 12 cans would be 12/2 * $1.00 = $6.00

Which is what he said, except that you are doing the calculation in a different order.

By his approach, the price of one can is half the price of two cans: $1.00/2 = $0.50.

So the price of 12 cans is 12 times that, $0.50 * 12 = $6.00.

This version of the calculation is $1.00/2 * 12, whereas you are doing 12/2 * $1.00 - 6 * $1.00 = $6.00. The result is the same, but your explanation doesn't fit the order of the calculation.

 

[Explain this!]

Which is what he said, except that you are doing the calculation in a different order.

By his approach, the price of one can is half the price of two cans: $1.00/2 = $0.50.

So the price of 12 cans is 12 times that, $0.50 * 12 = $6.00.

This version of the calculation is $1.00/2 * 12, whereas you are doing 12/2 * $1.00 - 6 * $1.00 = $6.00. The result is the same, but your explanation doesn't fit the order of the calculation.

Okay, I understand now. Thank you for correcting me! I did not originally think of the calculation as he did.