
#1
May 13th, 2017,
10:30
How much pure disinfectant must be added to 30 gallons of an 8% solution to increase its strength by 25%?
Let x = pure disinfectant to be added
The word PURE tells me that 100 will be in the equation somewhere.
30 gallons of 8 percent = 0.08(30)
Must be added to some unknown = plus x
My equation is 0.08(30) + x = 0.25(x + 100)
Correct? If not, can someone break this mixture problem step by step leading to the right equation?

May 13th, 2017 10:30
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Pessimist Singularitarian
#2
May 13th, 2017,
10:43
The LHS of your equation is correct, however for the RHS, we want the concentration to be increase BY 25%, not TO 25%, which means instead of 8%, we want 1.25*8% = 10%. Also, the amount of the final solution will be x + 30, not x + 100...so the correct equation, at least for the way I am interpreting the problem, is:
0.08(30) + x = 0.1(x + 30)

#3
May 13th, 2017,
14:05
Thread Author
0.08(30) + x = 0.1(x + 30)
2.4 + x = 0.1x + 3
x  0.1x = 2.4 + 3
0.9x = 5.4
x = 5.4/0.9
x = 6
So, 6 pure disinfectant must be added.
Correct?

Pessimist Singularitarian
#4
May 13th, 2017,
14:12
Originally Posted by
RTCNTC
0.08(30) + x = 0.1(x + 30)
2.4 + x = 0.1x + 3
x  0.1x = 2.4 + 3
You've subtracted 2.4 from the LHS, but added 2.4 to the RHS...

#5
May 13th, 2017,
14:16
Thread Author
0.08(30) + x = 0.1(x + 30)
2.4 + x = 0.1x + 3
x  0.1x = 2.4 + 3
0.9x = 0.6
x = 0.6/0.9
x = 0.66
Right?

Pessimist Singularitarian
#6
May 13th, 2017,
14:19
Originally Posted by
RTCNTC
0.08(30) + x = 0.1(x + 30)
2.4 + x = 0.1x + 3
x  0.1x = 2.4 + 3
0.9x = 0.6
x = 0.6/0.9
x = 0.66
Right?
If you are going to round to 2 decimal places then x ≈ 0.67 gal., otherwise x = 2/3 gal.
x = 0.6/0.9 = 6/9 = 2/3

#7
May 13th, 2017,
14:49
Thread Author
Originally Posted by
MarkFL
If you are going to round to 2 decimal places then x ≈ 0.67 gal., otherwise x = 2/3 gal.
x = 0.6/0.9 = 6/9 = 2/3
Great as always.