Respuesta :
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.
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.
