Question

Joe and JoAnn each bought 12 ounces of coffee in a 16 ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee

Answer 1

`Ratio = 7:6`

Explanation:

Given

Initially

`Joe = 12oz` -- coffee

`JoAnn = 12oz` -- coffee

Joe drank 2oz coffee; So, we have:

`Joe = 12oz - 2oz`

`Joe = 10oz` --- coffee

Joe added 2oz cream; So, we have:

`Joe = 10oz` --- coffee
`Joe = 2oz` --- cream

JoAnn added 2oz cream and stirred. So, we have:

`Joe = 12oz` --- coffee
`JoAnn = 2oz` --- cream

`Total = 14oz`

JoAnn drank 2oz from the drink; the amount of drink JoAnn drank is:

`JoAnn = (Cream)/(Total)`

`JoAnn = (2)/(14)`

`JoAnn = (1)/(7)`

Amount of cream left is:

`Amount = [1- (1)/(7)] *2`

Take LCM

`Amount = [(7-1)/(7)] * 2oz`

`Amount = (6)/(7) * 2oz`

`Amount = (12)/(7)oz`

So, we have:

`Joe = 2oz` --- cream

`JoAnn = (12)/(7)` cream

The ratio is:

`Ratio = 2:(12)/(7)`

Multiply by 7

`Ratio = 14:12`

Divide by 2

`Ratio = 7:6`