The coffee jug hold four times as much as the milk jug everyone has the same sized cup but each person likes different amounts of milk in thier coffee jane likes half milk and half coffee jean june joan each like one quarter milk and ian drinks black coffee they fill up thier five cups the way the each like it and just empty one of the jugs how much liquid is left in the other

We will assume that each of their cups holds exactly 1 cup of liquid. Let m represent milk and c represent coffee.

Jane = 1/2m + 1/2c to represent 1/2 milk and 1/2 coffee

Jean, June, and Joan = 3 (1/4m + 3/4c) [they all 3 like the same ratio, so multiply the expression by 3], to represent 1/4 milk and 3/4 coffee

Ian = 1c (since he likes black coffee, his entire 1-cup dish of coffee will be coffee)

Adding these together we have:

1/2m + 1/2c + 3 (1/4m + 3/4c) + 1c

= 1/2m + 1/2c + 3/4m + 9/4c + 1c

Find a common denominator:

= 2/4m + 2/4c + 3/4m + 9/4c + 1c

Convert the 1 whole to a fraction:

= 2/4m + 2/4c + 3/4m + 9/4c + 4/4c

Combine your m's:

= 5/4m + 2/4c + 9/4c + 4/4c

Combine your c's:

= 5/4m + 15/4c

We know there is 4 times as much coffee as milk. Looking at the two fractions we have left, we can see that 15/4 = 3 (5/4). We would expect to see 4 (5/4), since there is 4 times as much coffee. That means we have 5/4 or 1 1/4 of the liquid left.