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

Answer:

Option D

the weights would be the best deal is $2\frac{7}{8}$

Step-by-step 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;

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

Now, convert these improper fraction into proper fraction.

$2\frac{2}{3}=\frac{8}{3}$

$2\frac{9}{11}=\frac{31}{11}$

$2\frac{4}{5}=\frac{24}{5}$

$2\frac{7}{8}=\frac{23}{8}$

To make their denominators same,

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

So,

$\frac{8}{3}= \frac{8\cdot 440}{3\cdot 440} =\frac{3520}{1320}$

$\frac{31}{11}= \frac{31\cdot 120}{11\cdot 120} =\frac{3720}{1320}$

$\frac{14}{5} =\frac{14\cdot 264}{5\cdot 264}= \frac{3696}{1320}$

$\frac{23}{8}=\frac{23\cdot 165}{8\cdot 165} =\frac{3795}{1320}$

As, you can see that the only fraction is greatest is $\frac{3795}{1320}$

therefore, the weight $2\frac{7}{8}$ would be the best deal.