Question

A machinist must cut 12 strips of metal that are each 2 ft

2 7/8 in. long. What is the total length needed in​ inches?

Answer 1

To find the total length needed in inches, we need to calculate the length of each strip and then multiply it by the number of strips.

Each strip is 2 ft 2 7/8 in long. We can convert the 2 ft to inches by multiplying it by 12 since there are 12 inches in 1 foot.

`\displaystyle\sf 2 \text{ ft} = 2 * 12 = 24 \text{ inches}`

Now we can add the 24 inches to the 2 7/8 inches:

`\displaystyle\sf 24 \text{ inches} + 2 (7)/(8) \text{ inches}`

To add these two numbers, we need to find a common denominator. The common denominator for 8 and 8 is 8.

`\displaystyle\sf 24 \text{ inches} + 2 (7)/(8) \text{ inches} = 24 \text{ inches} + (2 * 8 + 7)/(8) \text{ inches}`

Simplifying the fraction:

`\displaystyle\sf 24 \text{ inches} + (23)/(8) \text{ inches}`

Now we can add the inches:

`\displaystyle\sf 24 \text{ inches} + (23)/(8) \text{ inches} = (24 * 8)/(8) \text{ inches} + (23)/(8) \text{ inches}`

Combining the fractions:

`\displaystyle\sf (192)/(8) \text{ inches} + (23)/(8) \text{ inches}`

Adding the fractions:

`\displaystyle\sf (192 + 23)/(8) \text{ inches} = (215)/(8) \text{ inches}`

Therefore, each strip is
`\displaystyle\sf (215)/(8)` inches long.

To find the total length needed, we multiply the length of each strip by the number of strips:

`\displaystyle\sf \text{Total length} = \left((215)/(8) \text{ inches}\right) * 12 \text{ strips}`

Calculating the result:

`\displaystyle\sf \text{Total length} = (215 * 12)/(8) \text{ inches}`

`\displaystyle\sf \text{Total length} = (2580)/(8) \text{ inches}`

Simplifying the fraction:

`\displaystyle\sf \text{Total length} = 322.5 \text{ inches}`

Therefore, the total length needed in inches is 322.5 inches.