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.2 9/11 B.2 4/5 C.2 2/3 D.2 7/8

Answer 1

The correct option is: D.
`2(7)/(8)`

Step-by-step explanation

As the price of each meat package is same that is $12.99, so the best deal will be when the weight of the package will be greatest.

The weight are
`2(9)/(11), 2(4)/(5), 2(2)/(3)` and
`2(7)/(8)` pounds. For finding the fraction which has greatest value, first we will convert them into improper fraction and then make their denominators same. LCM of the denominators is 1320. So......

`2(9)/(11)= (31)/(11)= (31*120)/(11*120)=(3720)/(1320) \\ \\ 2(4)/(5)= (14)/(5)=(14*264)/(5*264)=(3696)/(1320)\\ \\ 2(2)/(3)=(8)/(3)=(8*440)/(3*440)=(3520)/(1320)\\ \\ 2(7)/(8)=(23)/(8)=(23*165)/(8*165)=(3795)/(1320)`

We can see that 3795 is the greatest numerator. So,
`2(7)/(8)` has the greatest value.

Thus, the best deal will be
`2(7)/(8)` pounds.