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? Original Added New Amount of Detergent 1.98 gallons 0 Amount of Solution 11 gallons g

Answer 1

                                       Original                              Added                         New Amount of Detergent    1.98 gallons                           0                         1.98

Amount of Solution      11 gallons                                 g                   11+g

Given Meryl needs to add enough water to 11 gallons of an 18% detergent solution to make a 12% detergent solution.

[tex]\frac{1.98}{11+g}=\frac{12}{100}

Answer 2

Thank you for asking this question.

We need a quantity of a pure detergent in this question.

We will first treat the 11 gallons with an 18% solution.

And 18% of that or approximately 1.98 gallons, is pure detergent,

and the remaning of these 11 will be water that means and that would be 9.02 gal

Now we will add x gallons of water to this solution to obtain (11+x) gallons of a 12% solution.

Now we need to find x

(11 gallons + x)(0.12) = (11 gallons)(0.18)

When we divide both sides by 0.12, we will get     

(11 gallons + x) = (11 gallons)(1.5)

Now we will Multiply both sides by 10,

we get 110 gallons + 10x = (11 gallons)(15)

Then 10x = 165 gallons - 110 gallons, or 55 gallons.

Divide both sides by 10, we get x = 5.5 gallons (Answer)