Answer:
1) 2 lbs
2) 0.17 lbs
3) 9.5 lbs
Step-by-step explanation:
Amount of sugar Ella has = 0.5 lbs
Let the amount of water she adds to make the solution = x lbs
So total amount of the mixture would be = (x + 0.5) lbs
Case 1: 20% syrup
20% syrup means the sugar percentage in the mixture should be 20% of the entire mixture. So, 0.5 should be 20% of (x + 0.5). In equation form this can be written as:
0.5 = 20% of (x + 0.5)
0.5 = 0.2(x + 0.5)
Dividing both sides by 0.2, we get:
2.5 = x + 0.5
x = 2 lbs
This means, 2 lbs of water should be added to make 20% syrup solution. So, total syrup she would have will be 2.5 lbs.
Case 2: 75% syrup
75% syrup means the sugar percentage in the mixture should be 75% of the entire mixture. So, 0.5 should be 75% of (x + 0.5). In equation form this can be written as:
0.5 = 75% of (x + 0.5)
0.5 = 0.75(x + 0.5)
Dividing both sides by 0.75, we get:
0.67 = x + 0.5
x = 0.17 lbs
This means, 0.17 lbs of water should be added to make 75% syrup solution. So, total syrup she would have will be 0.67 lbs.
Case 3: 5% syrup
5% syrup means the sugar percentage in the mixture should be 5% of the entire mixture. So, 0.5 should be 5% of (x + 0.5). In equation form this can be written as:
0.5 = 5% of (x + 0.5)
0.5 = 0.05(x + 0.5)
Dividing both sides by 0.05, we get:
10 = x + 0.5
x = 9.5 lbs
This means, 9.5 lbs of water should be added to make 5% syrup solution. So, total syrup she would have will be 10 lbs.
