QuestionMax bought two rolls of 18 inches and 30 inches. How many equal sections can they be cut into?

Studdy Solution

STEP 1

Assumptions1. The length of the first sandwich roll is18 inches. . The length of the second sandwich roll is30 inches.
3. The rolls are to be cut into equal sections of maximum possible length.
4. The number of sections is the total length divided by the length of each section.

STEP 2

First, we need to find the greatest common divisor (GCD) of the lengths of the two rolls. This will give us the length of each section. The GCD can be found using the Euclidean algorithm.
$GCD(18,30)$

STEP 3

To find the GCD using the Euclidean algorithm, we subtract the smaller number from the larger number, and then replace the larger number with the result. We repeat this process until the two numbers become equal.
$GCD(30 -18,18) = GCD(12,18)$

STEP 4

We repeat the process again.
$GCD(18 -12,12) = GCD(6,12)$

STEP 5

We repeat the process one more time.
$GCD(12 -,) = GCD(,)$

STEP 6

Now the two numbers are equal, so the GCD is6. This means each section will be6 inches long.

STEP 7

Now that we have the length of each section, we can find the total number of sections by dividing the total length of the rolls by the length of each section.
$Total\, sections = Total\, length / Length\, of\, each\, section$

STEP 8

The total length of the rolls is the sum of the lengths of the two rolls.
$Total\, length = Length\, of\, first\, roll + Length\, of\, second\, roll$

STEP 9

Plug in the values for the lengths of the two rolls to calculate the total length.
$Total\, length =18\, inches +30\, inches$

STEP 10

Calculate the total length.
$Total\, length =18\, inches +30\, inches =48\, inches$

STEP 11

Now, plug in the values for the total length and the length of each section to calculate the total number of sections.
$Total\, sections =48\, inches /6\, inches$

STEP 12

Calculate the total number of sections.
$Total\, sections =48\, inches /6\, inches =8\, sections$ Max will have8 sections in all.

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