Problema Solution
a chemist needs to make 30 ounces of a 3o% alcohol solution by mixing a 15% alcohol solution with a 40%alcohol solution. How many ounces of the 40% solution does she need?
Answer provided by our tutors
Let x be the amount of the 15% solution needed and y be the amount of 40% solution needed. From the question, we can write the following equations:
.15x+.4y=.3(30)
x+y=30
In the first equation, the percentages (15, 4, and 30) were converted to decimals by dividing by 100.
Since we have two equations with two unknowns, we can now solve the problem by solving the system of equations.
First, solve for x in the second equation.
x=30-y
Second, plug this into the first equation to get 1 equation with 1 unknown.
.15(30-y)+.4y=.3(30)
Now, solve this for y.
4.5-.15y+.4y=9
.25y=4.5
y=18
Therefore, the chemist will need 18 ounces of the 40% solution.