Question

A catering company needs 8.75 lb of shrimp for a small party. They buy `3 2/3` lb of jumbo shrimp, `2 5/8` lb of medium-sized shrimp, and some mini-shrimp. How many pounds of mini-shrimp do they buy?

Answer 1

Given with a lot of explanation

`2 11/24color(white)(.)^("lb")` of mini-shrimp

Explanation:

Needs a total of `8.75^("lb")->8 3/4color(white)()^("lb")`
Bought: `3 2/3 + 2 5/8`

So needs to purchase a further: `8 3/4 -3 2/3-2 5/8`

I choose to use a common denominator of 24 for the fraction parts
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Considering "8 3/4)`

Write as `8+ 3/4`

`8+3/4" "->" "8+(3/4xx1)" "->" "8+(3/4xx6/6)`

`" " =" "8 18/24`
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`color(blue)("Considering "3 2/3)`

Write as `3+ 2/3`

`3+ 2/3" " ->" "3+(2/3xx1)" "->" "3+(2/3xx8/8)`

`" "=3 16/24`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Considering "2 5/8)`

Write as `2+ 5/8`

`2+ 5/8" "->" "2+(5/8xx1)" "->" "2+(5/8xx3/3)`

`" "=2 15/24`
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`color(blue)("Putting it all together")`

`8 (color(red)(18))/24-3 (color(green)(16))/24-2 (color(green)(15))/24`

Notice that `color(green)(16+15 >)color(red)( 18)` so write `8 18/24` as `7 42/24` giving:

`7 42/24-3 16/24 - 2 15/25`

Dealing with just the whole numbers bit:
`7-3-2 = +2`

Dealing with the fraction part:

`(42-16-15)/24 = 11/24`

Putting all together we have the answer of:

`2 11/24`