Systems of equations work problem.

Question

A chemist had two solutions: a 50% methane solution and an 80% methane solution. He wants 100 mL of a 70% methane solution. How many mL of each solution does he need?

Answer 1

You want to mix 2 solutions and have them average out to 70%

Equal amounts would average 65% since (50+80)/2 = 65

That leads to one equation.

The other is amount of Fifty% + amount of Eighty% = 100ml.

 

So Volumes:   VF + VE = 100

and percents: [ VF(0.50) + VE(0.80) ] ÷ 2 = 0.70

 

Two equations, Two unknowns, solve foe VF and VE

Another way is to set up a table:

percent X Amount of Mixture = Quantity of Substance

1) 0.50 V50 0.50 x V50

2) 0.80 100 ml - V50 0.80 x (100 ml - V50)

 total 0.70 100 ml ( 0.50 x V50) + (0.80 x (100 ml - V50) )

equation: 0.70 X 100 ml = ( 0.50 x V50) + (0.80 x (100 ml - V50) )

solve for the amount V50 then find the amount of V80