The coffee jug holds 4 times as much as the milk jug everyone has the same size cup but each person likes different amounts of milk in thier coffee jane likes half mulk and half coffee jean june and joan each like one quarter milk and ian drinks black coffee they fill up their five cups the way they each like and just empty one of the jugs how much luquid is left over

We will assume that the coffee cups hold 1 cup of total liquid each. Use the variable m to represent milk and c to represent coffee. Jane likes 1/2 milk, so 1/2m, and 1/2 coffee, or 1/2c. Jean, June and Joan each like 1/4 milk, or 1/4m, and 3/4 coffee, or 3/4c. Ian likes all coffee, and since 100% is the whole number 1, we will represent that as 1c. We will combine our like terms, which is adding our m's together and then adding our c's together. We have 1/2m, 1/4m, 1/4m, 1/4m (remember, these are for Jean, June and Joan), and no m's for Ian. In order to add these we will need a common denominator. The lowest common denominator (LCD) for 1/2 and 1/4 is 4. Converting 1/2 to something over 4 means we multiply top and bottom by 2 (2*2 = 4), so we have 2/4m. Now we have 2/4m + 1/4m + 1/4m + 1/4m = 5/4m.

For our coffee, we have 1/2c + 3/4c + 3/4c + 3/4c + 1c. Again we need a common denominator. Since we have 1/2 and 1/4 again, we will use 4. We multiply top and bottom of 1/2 by 2 (remember 2*2 = 4) and have 2/4c + 3/4c + 3/4c + 3/4c + 4/4c (if the numerator and denominator is the same, it is equal to one whole or 1). This gives us 15/4c.

Comparing the amount of milk to the amount of coffee, 5/4m to 15/4c, we can see that 15 is 3 times as much as 5, so we have 3 times as much coffee used as milk. We know that there is 4 times as much coffee as milk. 5/4 * 4/1 (remember to put whole numbers over 1 to multiply it by a fraction) would give us 20/4. This means we have 20/4 - 15/4 or 5/4 cups of liquid left. (5/4 would simplify to 1 and 1/4 cups of liquid left.)