Question

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

A. 1.98/11+g - 12/100 = 1
B. 1.98/11+g + 12/100 = 1
C. 11+g/1.98 = 12/100
D. 1.98/11+g = 12/100

Answer 1

D. 1.98/11+g = 12/100

Explanation:

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

(Gallons)

Added

(Gallons)

New

(Gallons)

Amount of Detergent

1.98

0

Amount of Solution

11

g

StartFraction 1.98 Over 11 + g EndFraction minus StartFraction 12 Over 100 EndFraction = 1

StartFraction 1.98 Over 11 + g EndFraction + StartFraction 12 Over 100 EndFraction = 1

StartFraction 11 + g Over 1.98 EndFraction = StartFraction 12 Over 100 EndFraction

StartFraction 1.98 Over 11 + g EndFraction = StartFraction 12 Over 100 EndFraction

Answer 2

The problem is about adding water to detergent solution to make a detergent solution.

In the problem g is taken for the number of gallons of water.

So, we can rephrase the given problem in simple words as

g gallons of water is added to 11 gallons of 18% detergent solution to get 12% detergent solution.

Let us write it in form of an equation,

g gallons of water is being added to 11 gallons of solution.

The total amount of solution will be (11 + g) gallons.

11 gallons of 18% detergent solution = 12% detergent solution.

For percent we can write over 100.

Therefore, above equation can be written as

11 × 18/100 = 12/100(g+11)

11 time 18 = 198

Therefore,

198/100 = 12/100(g+11)

Converting 198/100 into decimals, we get 1.98

We can rewrite above eqaution as

1.98 =12/100(g+11)

Dividing both sides by (g+11), we get

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

Therefore, correct option is D. 1.98/11+g = 12/100.