MATH SOLVE

5 months ago

Q:
# How many ML of a 35% acid mixture and a 95% acid mixture should be mixed to get 120 ML of a 40% acid mixture?

Accepted Solution

A:

ANSWER:
110ML of 35% acid solution must be mixed with 10ML of 95% solution to obtain 120ML of 40% solution.
SOLUTION:
First, set up table. fill in the unknowns with variables x and y. The table is attached below.From the table shown below, we can easily set up the two equations. Sum of values of two acids = Value of mixture 0.35x + 0.95y = 48 For convenience, we will multiply the entire equation by 100,
35 x + 95y = 4800 ------ (1) Now, Sum of amounts of each acid = Amount of mixture x + y = 120 --------- (2)
Multiply eqn 2 with 35 for easy calculation and derive the equation into one variable.
35 = 35x + 35y = 4200 Subtracting equation (2) from (1), we get
0 + 60y = 600 Thus, 60y = 600 [tex]y = \frac{600}{60} = 10[/tex]Substituting y = 10 in (2),
35x + 35(10) = 4200 35x + 350 = 4200 35x = 4200 - 350 35x = 3850 [tex]x = \frac{3850}{35} = 110[/tex]So, we have x = 110 and y = 10
We can conclude that 110ML of 35% acid solution must be mixed with 10ML of 95% solution to obtain 120 ML of 40% solution.