<span>let x = the number of liters of the 20% solution.
let y = the number of liters of the 60% solution.
you want x + y to be equal to 40 liters.
x is the number of liters total in the first solution. y is the number of liters total in the second solution.
you want .2 * x + .6 * y to be equal to .35 * 40
.2 * x is the number of liters of acid in the first solution. .6 * y is the number of liters of acid in the second solution. .35 * 40 is the number of liters of acid in the final solution.
you have two equations that need to be solved simultaneously.
they are:
x + y = 40 .2x + .6y = .35*40
simplify these equations to get:
x + y = 40 .2x + .6y = 14
you can solve by substitution or by elimination or by graphing. i will solve this one by graphing. this means to graph both equations and find the intersection.
the graph looks like this:
the graph says the intersection is at the coordinate point of (25,15).
this means that x = 25 and y = 15.
x is the number of liters of the 20% solution. y is the number of liters of the 60% solution.
the formula of .2x + .6y = 14 becomes .2 * 25 + .6 * 15 = 14. simplify this equation to get 14 = 14. this confirms the solution is good. </span>
