Question

Darryl wants to add enough water to 8 gallons of a 10% bleach solution to make a 5% bleach solution. which equation can he use to find x, the number of gallons of water he should add? original (gallons) added (gallons) new (gallons) amount of bleach 0.8 0 0.8 amount of solution 8 x 8 x startfraction 0.8 over 8 x endfraction times startfraction 5 over 100 endfraction = 1 startfraction 0.8 over 8 x endfraction times = startfraction 5 over 100 endfraction startfraction 0.8 over 8 x endfraction = startfraction 100 over 5 endfraction startfraction 0.8 over 8 x endfraction divided by startfraction 5 over 100 endfraction = 1

1. diemthu
0.80 = (x + 8)(0.05) is the equation used to find x.
Given,
Darryl has a solution of bleach with the concentration of 10%.
10% bleach solution means in 100 ml solution amount of bleach is 10 gm
Here,
Darryl wants to change the concentration of this solution to 5%, means he wants to add water so that amount of liquid will change but amount of bleach in grams will remain the same.
Amount of bleach in 8 gallons of 10% solution of bleach will be = (Volume)×(concentration) = 8(.10) gm
Let Darryl adds x gallons of water in 10% solution of bleach to make it 5% solution of bleach.
Amount of bleach in 5% solution of bleach = (x + 8)(0.05) gm
Now in both the concentrations of bleach solution amount of bleach will remain same.
So, 0.8 = (x + 8)(0.05) will be the equation from which he can find the value of x.