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. $2\frac{7}{8}$

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  $2\frac{9}{11}, 2\frac{4}{5}, 2\frac{2}{3}$ and $2\frac{7}{8}$ 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......

$2\frac{9}{11}= \frac{31}{11}= \frac{31*120}{11*120}=\frac{3720}{1320} \\ \\ 2\frac{4}{5}= \frac{14}{5}=\frac{14*264}{5*264}=\frac{3696}{1320}\\ \\ 2\frac{2}{3}=\frac{8}{3}=\frac{8*440}{3*440}=\frac{3520}{1320}\\ \\ 2\frac{7}{8}=\frac{23}{8}=\frac{23*165}{8*165}=\frac{3795}{1320}$

We can see that 3795 is the greatest numerator. So, $2\frac{7}{8}$ has the greatest value.

Thus, the best deal will be $2\frac{7}{8}$ pounds.