word problem

Question

A solution containing 25% alcohol is to be mixed with a solution containing 60% alcohol to make 200L of a solution containing 40% alcohol. I x is the amount of 25% solution needed and y is amount of 60% solution needed, write two equations relating x and y.

Answer 1

Hi Shakeya.

 

X = total volume of 25% EtOH

Y = total volume of 60% EtOH

 

The problem states that you need 200L of solution at the end, so that means that summing up the volumes of X and Y must result in 200:

 

X + Y = 200

 

Every liter of 25% alcohol contributes 0.25 liters of pure EtOH. Every liter of 60% alcohol contributes 0.60 liters of pure EtOH. You need 200L of 40% alcohol, meaning you need a grand total of:

 

200*0.40 = 80L of pure EtOH.

 

So:

 

X*0.25 + Y*0.60 = 80

 

Multiply both sides by 100 to clear up the decimals.

 

25X + 60Y = 8000

 

So your two equations are:

 

X + Y = 200

25X + 60Y = 8000

 

Hope this helps.