Respuesta :
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.)
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.)
Answer:
Correct answer (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.)
Step-by-step explanation:
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