A tank has a capacity of 10 gallons. When it is full it contains 15% alcohol. How many gallons must be replaced by an 80% solution to goive 10 gallons of a 70% solution?

8.46 gallons needed to be replaced

Step-by-step explanation:

Let x be the alcohol amount that replaced

-Original has concentration of 15% multiply by the amount of 10, which is equal to (0.15*10).

-Removed has concentration of 15% multiply by the amount of x, which is equal to (0.15 * X).

-Added has concentration of 80% multiply by the amount of X, which is equal to (0.8 * X).

-Solution has concentration of 70% multiply by the amount of 10, which is equal to (0.70*10).

So that, the equation will be:

Solution=Original + added - removed

7=1.5+0.8x-0.15x

7-1.5=0.65x

0.65x=55

x=55/0.65

x=8.46

8.46 gallons needed to be replaced.