Question

Lois is baking pies and cakes for a family party. The pie recipe calls for 2/3 cups of vegetable oil and the cake recipe calls for 1 1/6 cups of vegetables oil. If Lois wants to bake 2 pies and 2 cakes, how many cups of vegetable oil does she need?

Answer 1

2 pies need `4/3" cups" -> 1 1/3" cups"`

2 cakes need `22/6" cups" -> 3 2/3" cups"`

Explanation:

Let the count of cups of oil for pies be `p`
Let the count of cups of oil for cakes be `c`

Using ratio

Pies`-> ("cups of oil")/("count of pies") = (color(white)(.)2/3color(white)(.))/1-=p/2`

#color(green)([(color(white)(.)2/3color(white)(.))/1 color(red)(xx1)] = color(green)([(color(white)(.)2/3color(white)(.))/1 color(red)(xx2/2)] = ( color(white)(.)4/3color(white)(.))/2#

So 2 pies need `4/3" cups" -> 1 1/3" cups"`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Cakes`->("cups of oil")/("count of cakes") =(color(white)(.)11/6color(white)(.))/1 -=c/2`

#color(green)([(color(white)(.)11/6color(white)(.))/1 color(red)(xx1)] = [(color(white)(.)11/6color(white)(.))/1 color(red)(xx2/2)] =(color(white)(.)22/6color(white)(.))/2#

So 2 cakes need `22/6" cups" -> 3 2/3" cups"`