Eleanor and her little sister Joanna are responsible for two chores on their family's farm, gathering eggs and collecting milk. Eleanor can gather 15 dozen eggs or collect 5 gallons of milk per week. Joanna can gather 2 dozen eggs or collect 2 gallons of milk per week.

a. The family wants 2 gallons of milk per week and as many eggs as the sisters can gather. Currently, they collect one gallon of milk each and as many eggs as they can. How many dozens of eggs does the family have per week?

dozen eggs.

b. If the sisters specialized, which sister should collect the milk?

c. If the sisters specialized, how many dozens of eggs would the family have per week?

dozen eggs

The answer to a) is 13 dozens; answer to b) is 11 dozens, and answer to c) is 15 dozens

Explanation:

Let eggs be x and Milk be y

Eleanor = 15x or 5y

Sister = 2x or 2y

Eleanor 15x=5y; i. e. y=3x

Sister 2x=2y; i. e. x=y

a) Each collected 1 gallon of milk

Meaning Eleanor had 4 more gallons to collect and each gallon is equivalent to 3 dozens

So she gathered 4*3=12 dozens of eggs

The sister gathered 1 dozen of eggs

Totals = 12+1=13 dozens.

b) If they specialize:

Eleanor to collect milk 2 gallons

Time to collect the remaining 3 gallons be spend for eggs i. e. 3*3 = 9 dozens

Sister spend time in collecting eggs i. e. 2 dozens

Total = 2+9=11dozens

c) If the sister specializes in collecting milk

She will collect milk only while Eleanor will gather eggs alone i. e. 15 dozens

Hence, Eleanor should specialize in eggs.

The family will have 15 dozens at the end of the week.