One morning each member of angelas family drank an 8-ounce mixture of coffee with milk. The amounts of coffee and milk varied from cup to cup, but were never zero. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. How many people are in the family?
Answers
Given:
One morning each member of angelas family drank an 8-ounce mixture of coffee with milk.
The amounts of coffee and milk varied from cup to cup, but were never zero.
Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee.
To find:
How many people are in the family?
Solution:
From given, we have,
Each member of angelas family drank an 8-ounce mixture of coffee with milk.
Let c represents the coffee, m represents the milk and p be the people.
Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee.
⇒ Angela drank m/4 of milk and c/6 of coffee.
As each member drank the same amount of coffee, so we obtained an equation,
(c/6 + m/4)p = c + m
2c(6 - p) = 3m(p - 4)
as both c and m are positive, so, we have to satisfy the condition,
(6 - p) > 0 and (p - 4) > 0
6 > p and p > 4
So, 5 is the correct number of people.
Therefore, there are 5 people are in the family.