Question

7. A hospital supply room only has a 70% hydrogen peroxide solution and a 90% hydro-

gen peroxide solution. How many liters of each should be mixed to obtain 50 liters
of a 85% solution? You must set up an equation and solve to receive credit.

Answer 1

Answer: 12.5 liters of 70% hydrogen peroxide solution and 37.5 liters of 90% hydrogen peroxide solution is required.

Explanation:

Let x = Quantity of 70% hydrogen peroxide solution.

y = Quantity of 90% hydrogen peroxide solution.

To obtain: 50 liters of a 85% solution.

x+y =50 (i) (Total quantity of solution)

0.70x+0.50y=0.85(50) (Total quantity of hydrogen peroxide)

⇒ 0.70x+0.50y= 42.5 (ii)

Multiply 0.70 to (i) , we get

`0.70x+0.70y=0.70(50)\\\\\Rightarrow\ 0.70x+0.70y=35\ \ \ \ (iii)`

Subtract (iii) from (ii), we get

`0.20y=7.5\\\\\Rightarrow\ y=(7.5)/(0.20)\\\\\Rightarrow\ y=37.5`

Put value of y in (i) , we get

`x+37.5=50\\\\\Rightarrow\ x=50-37.5\\\\\Rightarrow\ x= 12.5`

Hence, 12.5 liters of 70% hydrogen peroxide solution and 37.5 liters of 90% hydrogen peroxide solution is required.