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 be added
bro. this sucks
im literally crying bc i cant find the anSWER
To find the equation that Meryl can use to determine the number of gallons of water to add, we can follow these steps:
Step 1: Understand the problem
Meryl needs to add water to a given amount of 18% detergent solution in order to create a 12% detergent solution. The goal is to find the number of gallons of water she should add.
Step 2: Set up the equation
Let's denote the number of gallons of water Meryl should add by "g". So, the final volume of the detergent solution will be the initial volume (11 gallons) plus the volume of water added (g gallons).
Step 3: Determine the detergent content
The detergent content in the initial solution (18%) and the desired solution (12%) can be represented as a decimal. We can express it as 0.18 for 18% and 0.12 for 12%.
Step 4: Set up the equation based on detergent content
The detergent content in the final solution can be calculated using the formula:
(initial detergent content * initial volume + added detergent in water * water volume) / final volume.
For the initial detergent solution, the equation becomes:
(0.18 * 11) / (11 + g)
For the water added, the equation becomes:
(0 * g) / (11 + g)
Step 5: Set up the equation based on the desired detergent content
In the final solution, the detergent content is desired to be 12%. So, we set up the equation as follows:
0.12 = [detergent content in the final solution] = (0.18 * 11) / (11 + g)
Step 6: Solve the equation for g
To find g, we can rearrange the equation by multiplying both sides by (11 + g) to eliminate the denominator:
0.12(11 + g) = 0.18 * 11
Simplifying the equation:
1.32 + 0.12g = 1.98
Next, we isolate the variable g:
0.12g = 1.98 - 1.32
0.12g = 0.66
g ≈ 5.5
Therefore, Meryl should add approximately 5.5 gallons of water to the 11 gallons of 18% detergent solution to obtain a 12% detergent solution.
Don't know the choices, but one equation is
.18(11) = .12(11+g)