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

Answer:

$Ratio = 7:6$

Step-by-step 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:

$JoAnn = \frac{Cream}{Total}$

$JoAnn = \frac{2}{14}$

$JoAnn = \frac{1}{7}$

Amount of cream left is:

$Amount = [1- \frac{1}{7}] *2$

Take LCM

$Amount = [\frac{7-1}{7}] * 2oz$

$Amount = \frac{6}{7} * 2oz$

$Amount = \frac{12}{7}oz$

So, we have:

$Joe = 2oz$ --- cream

$JoAnn = \frac{12}{7}$ cream

The ratio is:

$Ratio = 2:\frac{12}{7}$

Multiply by 7

$Ratio = 14:12$

Divide by 2

$Ratio = 7:6$