Problema Solution
SET UP A SYSTEM OF LINEAR EQUATIONS IN TWO VARIABLES AND SOLVE FOR THE UNKNOWN QUANTITIES.
A pharmacist must mix a 10% solution of a drug with some 60% solution to get 18 liters of a 35% mixture. How many liters of the 10% solution and the 60% solution must you mix to get 18 liters of the 35% mixture?
Answer provided by our tutors
Let x liters of the 10% solution be used, and y liters of the 60% solution be used.
Now, the total volume of the mixture = (x + y) liters
It is given that: x + y = 18 ... equation (1)
Again, 10% * x + 60% * y = 35% * 18
0.1x + 0.6y = 6.3
x + 6y = 63 ... equation (2)
Subtracting eq(1) from eq(2), we get:
x + 6y - (x + y) = 63 - 18
5y = 45
y = 45/5
y = 9
Substituting y = 9 in equation (1), we get:
x + 9 = 18
x = 18 - 9
x = 9
So, 9 liters of the 10% solution should be mixed with 9 liters of the 60% solution to get 18 liters of the 35% mixture.