Question

Meryl needs to add enough water to 11 gallons of an 18% detergent solution to make a 12% detergent solution. Which equation can she use to find g, the number of gallons of water she should add?

Answer 1

The amount of detergent is 11 * 0.18 = 1.98 gallons.
When g gallons of water is added to the 11 gallons of solution, the total amount of solution will be (11 + g) gallons. If the (11 + g) gallons is to be a 12% solution, the following equation applies:
0.12(11 + g) = 1.98
which simplifies to:
1.32 + 0.12g = 1.98
giving
0.12g = (1.98 - 1.32) gal.
and finally
\[\large g=\frac{(1.98-1.32)}{0.12}\ gal.\]