Question

solving mixture problems
shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. the table shows the amount of each solution used.

bleach solution	cups	bleach concentration	total
25% bleach	x	0.25	0.25x
mixture	5 + x	0.20	3

what is the value of x?
options: 24, 1, 10

Explanation:

Step1: Set up the equation from the total bleach

The total bleach from the mixture should equal the sum of the bleach from each solution. So, \(0.5 + 0.25x = 3\) (since the total bleach in the mixture is 3, from the table).

Step2: Solve for x

Subtract 0.5 from both sides: \(0.25x = 3 - 0.5\)
Simplify the right side: \(0.25x = 2.5\)
Divide both sides by 0.25: \(x=\frac{2.5}{0.25}\)
Calculate the division: \(x = 10\)

Answer:

10