Question

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
10% Bleach
5
0.10
0.5
25% Bleach
0.25
0.25x
Mixture
0.20
What is the value of x?
What is the value of x?

Answer 1

10

Explanation:

0.25x + 0.10*5 = 0.20(x+5)

25x + 10*5 = 20x + 20*5

5x = 10*5

x = 10 cups (amt. of 25% bleach used)

Answer 2

10

Explanation:

`\left[\begin{array}{cccc}Bleach\ solution&Cups\ bleach&Concentration&Total\\10\%\ Bleach&5&0.10&0.50\\25\%\ Bleach&x&0.25&0.25x\\Mixture&5+x&0.20&0.20(5+x)\end{array}\right]`

The total bleach in the mixture is 0.20 (5 + x), but it's also the sum of the bleach amounts in each solution: 0.50 + 0.25x.

Therefore:

0.20 (5 + x) = 0.50 + 0.25x

1 + 0.20x = 0.50 + 0.25x

0.50 = 0.05x

x = 10