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

A suitable equation will equate the quantity of detergent both before and after the water is added to the solution.

the amount of detergent in 11 gal of 18% solution is the same as the amount of detergent in the 12% solution (after g gallons of water are added)
.18*11 = .12*(11+g)

Answer 2

`(1.98)/(11+g)=(12)/(100)`

Explanation:

Given,

Total quantity of solution = 11 gallons

Initial detergent in the solution = 18 % of 11 gallons

`=(18* 11)/(100)`

`=(198)/(100)`

`=1.98\text{ gallons}`

Now, here g represents the number of gallons of water she should add to make 12 % detergent solution,

Final quantity of solution = ( 11 + g ) gallons

Thus, we can write,

The part of detergent in (11+g) gallons of water = The final percentage of detergent

`(1.98)/(11+g)=(12)/(100)`

Which is the required equation.