Question 1133340
x = 30% solution
y = 80% solution.


you want 6 liters of a 70% solution.


first equation is x + y = 6


second equation is .3 * x + .8 * y = .7 * (x + y)


in the first equation solve for y to get y = 6 - x


in the second equation replace y with 6 - x to get:


.3 * x + .8 * y = .7 * (x + y) becomes .3 * x + .8 * (6 - x) = .7 * (x + 6 - x)


simplify to get .3 * x + 4.8 - .8 * x = 4.2


combine like terms to get: -.5 * x + 4.8 = 4.2


subtract 4.8 from both sides of this equation to get -.5 * x = -.6


divide both sides of this equation by -.5 to get:


x = -.6/-.5 = 1.2


in the equation of x + y = 6, replace x with 1.2 and solve for y to get:


y = 6 - 1.2 = 4.8


x + y = 6 becomes 1.2 + 4.8 = 6 which becomes 6 = 6 which is true.


.3 * x + .8 * y = .7 * (x + y) becomes .3 * 1.2 + .8 * 4.8 = .7 * (1.2 + 4.8) which becomes .36 + 3.84 = .7 * 6 which becomes 4.2 = 4.2 which is true.


the solution looks good.


x = 1.2 and y = 4.8


x + y = 6 becomes 1.2 + 4.8 = 6 which is true.


.3 * x + .8 * y becomes .3 * 1.2 + .8 * 4.8 which becomes .36 + 3.84 which becomes 4.2


4.2 / 6 = .7 = 70% which satisfies the requirements of the problem.


1.2 liters of a 30% mixture added to 4.8 liters of an 80% mixture results in 6 liters of a 70% solution.