Question

Sam wants to make 4 gallons of vegetable bean soup. The recipe above makes 1/3 gallon of soup. Help Sam make his grocery list for the store by researching the items in the soup and their packaging to determine how much of each ingredient he will need.

Answer 1

As we have a recipe that is meant for 1/3 gallon of soup and we want to scale it to 4 gallons, we can finde the constant of proportionality dividing 4 by 1/3:

`k=(4)/((1)/(3))=4\cdot(3)/(1)=12`

This means that the amount of ingredients of the 1/3-gallon recipe has to be multiplied by 12 in order to know the amount for a 4 gallon recipe.

Navy beans:

For a 1/3 gallon soup, we needed 1 1/4 cups, so for a 4 gallon soup we need:

`(1(1)/(4))\cdot12=12+(12)/(4)=12+3=15`

We need 15 cups of navy beans.

Carrots:

For a 1/3 gallon soup, we needed 3/4 cups, so for a 4 gallon soup we need:

`(3)/(4)\cdot12=(36)/(4)=9`

We need 9 cups of carrots.

The same procedure (multiplying by 12) has to be applied to all the ingredients in order to make the grocery list for a 4 gallon soup.