Question

4. Gary buys a 3 pound bag of cat food every 3 weeks. Gary feeds his cat the same amount of food
each day. Which expression can Gary use to determine the number of pounds of cat food his cat
eats each year?

Answer 1

Answer:

Option A. $(\frac{7}{2})\frac{52}{3}$

Explanation:

The complete question is

Gary buys a 3 1/2 pound bag of cat food every 3 weeks. Gary feeds his cat the same amount of food each day. What expression could be used to determine the number of pounds of cat food his cat eats each year(1 year-52 weeks)

A. 7/2 x 52/3

B. 7/2 x 3/52

C. 3( 1/2 x 3/52 )

D. 3 ( 1/2 x 52/3 )

we can say that

The cat eats 3 1/2 pound bag of cat food every 3 weeks

Remember that

one year represent 52 weeks

so

using proportion

Find out the number of pounds of cat food his cat  eats in 52 weeks (one year)

$\frac{3\frac{1}{2}}{3}\ \frac{pounds}{weeks}=\frac{x}{52}\ \frac{pounds}{weeks}$

Convert mixed number to an improper fraction

$3\frac{1}{2}\ pounds=\frac{3*2+1}{2}=\frac{7}{2}\ pounds$

substitute

$\frac{\frac{7}{2}}{3}\ \frac{pounds}{weeks}=\frac{x}{52}\ \frac{pounds}{weeks}\\\\x=(\frac{7}{2})\frac{52}{3}\\\\x=\frac{364}{6}\ pounds$

Convert to mixed number

$\frac{364}{6}\ pounds=\frac{360}{6}+\frac{4}{6}=60\frac{2}{3}\ pounds$

therefore

The expression is $(\frac{7}{2})\frac{52}{3}$

The number of pounds of cat food his cat  eats each year is 60 2/3 pounds