Answer:
1. 20% - add 2 lbs of water to get 2.5 lbs of syrup
2. 25% - add 1.5 lbs of water to get 2 lbs of syrup
3. 1.5% - add 32.833 lbs of water to get 33.333 lbs of syrup
Step-by-step explanation:
Ella has 0.5 lbs of sugar. Let x lbs be the amount of water Ella should add to get the syrup.
1. 20% syrup:
0.5 lbs - 20%
x+0.5 lbs - 100%
Write a proportion:
[tex]\dfrac{0.5}{x+0.5}=\dfrac{20}{100}\\ \\0.5\cdot 100=(x+0.5)\cdot 20\\ \\50=20x+10\\ \\20x=50-10\\ \\20x=40\\ \\x=2\ lbs[/tex]
To get 20% syrup Ella should add 2 lbs of water. The total weight of strup is 2.5 lbs.
2. 25% syrup:
0.5 lbs - 25%
x+0.5 lbs - 100%
Write a proportion:
[tex]\dfrac{0.5}{x+0.5}=\dfrac{25}{100}\\ \\0.5\cdot 100=(x+0.5)\cdot 25\\ \\50=25x+12.5\\ \\25x=50-12.5\\ \\25x=37.5\\ \\x=1.5\ lbs[/tex]
To get 25% syrup Ella should add 1.5 lbs of water. The total weight of strup is 2 lbs.
3. 1.5% syrup:
0.5 lbs - 1.5%
x+0.5 lbs - 100%
Write a proportion:
[tex]\dfrac{0.5}{x+0.5}=\dfrac{1.5}{100}\\ \\0.5\cdot 100=(x+0.5)\cdot 1.5\\ \\50=1.5x+0.75\\ \\1.5x=50-0.75\\ \\1.5x=49.25\\ \\x=\dfrac{49.25}{1.5}\approx 32.833\ lbs[/tex]
To get 1.5% syrup Ella should add 32.833 lbs of water. The total weight of strup is 33.333 lbs.
