Question 466772
x = number of liters of 1% solution.
y = number of liters of 9% solution.
you want a total of 5 liters of 3.24% solution.
your first equation is:
x + y = 5
this tells you that the total amount of solution will be 5 liters.
your second equation is:
.01*x + .09*y = .0324*5
this tells you that the mix of x liters of 1% solution + y liters of 9% solution will equal 5 liters of 3.24% solution.
you need to solve these 2 equations simultaneously to get your answer.
the equations are:
x + y = 5
.01*x + .09*y = .0324*5
simplify the second equation to get:
.01*x + .09*y = .162
your 2 equations are now:
x + y = 5
.01*x + .09*y = .162
solve for x or y in the first equation and then substitute in the second equation.
from the first equation, solving for y gets:
y = 5 - x
substituting for y in the second equation gets:
.01*x + .09*(5-x) = .162
since you have reduced the second equation from 2 unknowns to one unknown by applying the substitution from the first equation, you can solve for x in the second equation.
simplify the second equation to get:
.01*x + .09*5 - .09*x = .162
combine like terms and simplify further to get:
-.08*x + .45 = .162
subtract .45 from both sides of this equation to get:
-.08*x = .162 - .45
simplify this to get:
-.08*x = -.288
divide both sides of this equation by -.08 to get:
x = -.288 / -.08
simplify this to get:
x = 3.6
use your first equation to derive that y will be equal to 1.4
you have:
x = 3.6 liters
y = 1.4 liters
x + y = 5 becomes 3.6 + 1.4 = 5 which becomes 5 = 5, confirming the values for x and y solve the first equation.
substituting in your second equation of:
.01*x + .09*y = .162 gets you:
.01*3.6 + .09*1.4 = .06 which becomes .036 + .126 = .162 which becomes .162 = .162, confirming the values for x and y solve the second equation.
the values of 3.6 for x and 1.4 for y have solved both equations simultaneously, so they're good.
your answer is:
you need 3.6 liters of the 1% solution and 1.4 liters of the 9% solution to make 5 liters of 3.24% solution.