how many gallons of 70% alcohol solution must be mixed with 30 gallons of 23% solution to obtain a solution that is 60% alcohol?

How do I solve this problem?

let the amount to be added be x gal

.7x + .23(30) = .6(30+x)
times 100
70x + 23(30) = 60(30+x)
70x + 690 = 1800 + 60x
10x = 1110
x = 111 gallons

Together a baseball and a football weigh 2.25 pounds, the baseball and a soccer ball weigh 1.25 pounds, and the football and the soccer ball weigh 2.50 pounds. How much does each of the balls weigh?

To solve this problem, you can use the method of mixtures. The idea is to find the proportion of the different solutions (70% alcohol and 23% alcohol) that need to be combined in order to get a desired concentration (60% alcohol). Here's the step-by-step solution:

Step 1: Write down the given information:
Let "x" represent the number of gallons of the 70% alcohol solution to be mixed.
Given: 30 gallons of 23% alcohol solution.
Desired concentration: 60% alcohol.

Step 2: Set up the equation:
The equation can be derived from the concept that the total amount of alcohol in the mixture should be the sum of the alcohol in each solution.
Alcohol in 70% solution + Alcohol in 23% solution = Alcohol in final mixture.

(0.7x) + (0.23 * 30) = 0.6 * (x + 30)

Step 3: Solve the equation:
Simplify the equation:
0.7x + 6.9 = 0.6x + 18

Rearrange the equation:
0.7x - 0.6x = 18 - 6.9
0.1x = 11.1

Divide both sides by 0.1:
x = 11.1 / 0.1
x = 111

Step 4: Answer the question:
To obtain a solution that is 60% alcohol, you need to mix 111 gallons of the 70% alcohol solution with 30 gallons of the 23% alcohol solution.