Question

Louis and Ollie are pricing meat at a butcher shop. All of the meat packages are marked $12.99, and the weight, in pounds, of each package is written as a mixed fraction. Which of the following weights would be the best deal? A. 22⁄3 B. 29⁄11 C. 24⁄5 D. 27⁄8

Answer 1

Option D

the weights would be the best deal is
`2(7)/(8)`

Explanation:

The price of all meat packages are marked $12.99.

To find the best deal we have to show that the weight of which package will be greatest.

The weight of each packages are written as a mixed fraction as follows;

`2(2)/(3) , 2(9)/(11) , 2(4)/(5) , 2(7)/(8)`

Now, convert these improper fraction into proper fraction.

`2(2)/(3)=(8)/(3)`

`2(9)/(11)=(31)/(11)`

`2(4)/(5)=(24)/(5)`

`2(7)/(8)=(23)/(8)`

To make their denominators same,

the LCM(Least common multiples) of the denominators(11, 3, 5, 8) is 1320.

So,

`(8)/(3)= (8\cdot 440)/(3\cdot 440) =(3520)/(1320)`

`(31)/(11)= (31\cdot 120)/(11\cdot 120) =(3720)/(1320)`

`(14)/(5) =(14\cdot 264)/(5\cdot 264)= (3696)/(1320)`

`(23)/(8)=(23\cdot 165)/(8\cdot 165) =(3795)/(1320)`

As, you can see that the only fraction is greatest is
`(3795)/(1320)`

therefore, the weight
`2(7)/(8)` would be the best deal.