Question 9800
1) Original bleach solution is: 100 gallons of 2% concentration. Remove x gallons of 2% concentration and add x gallons of 100% bleach to get 100 gallons of 5% concentration.  Let's set up the equation for this: Change percents to decimals.

{{{100(0.02) - x(0.02) + x(1) = 100(0.05)}}} Simplify and solve for x.

{{{2 - 0.02x + x = 5}}}

{{{2 + 0.98x = 5}}}

{{{0.98x = 3}}}

{{{x = 3.06}}}

Approximately 3.06 gallons of the original solution should be drained and replaced with bleach to attain the recommended level of concentration of 5%.

2)Original fruit punch is 750 ml of 50% concentration of pure fruit juice.  Jill removes 100 ml of the 50% concentration and add 100 ml of x% concentration to get 750 ml of 48% concentration. Change the percents to decimals and set up the equation:

{{{750(0.5) - 100(0.5) + 100(x) = 750(0.48)}}} Simplify and solve for x.

{{{375 - 50 + 100x = 360}}}

{{{100x = 35}}}

{{{x = 0.35}}}

0.35 = 35%

The cheaper brand of punch had 35% concentration of pure fruit juice.