Question

Thirty liters of a 40% acid solution is obtained by mixing a 25% solution with a 50% solution.
(a) Write a system of equations in which one equation represents the amount of final mixture required and the other represents the percent of acid in the final mixture. Let x and y represent the amounts of the 25% and 50% solutions, respectively.
(b) Use a graphing utility to graph the two equations in part (a) in the same viewing window. As the amount of the 25% solution increases, how does the amount of the 50% solution change?
(c) How much of each solution is required to obtain the specified concentration of the final mixture?

Answer 1

Answer:

18 parts of the 25% acid solution and 12 parts of the 50% acid solution

Step-by-step explanation:

(a) Let the system of equations be

(1) A × x + B × y = 0.4 × 30

and A + B = 30

where x = 25% acid solution and y = 50% acid solution

Simplifying, we get

A × 0.25 + B × 0.5 = 0.4 × 30 = 12

or (i)A + 2 × B = 48

and (ii) A + B = 30

b) See the attached graph

as the 25% acid solution is increasing the 50% acid solution also increases

c) From the equations

(i)A + 2 × B = 48

and (ii) A + B = 30

we get from equation (ii) A = 30 - B

Substituting for A in equation (i) we get

A + 2 × B = 48 ▶ 30 - B + 2 × B = 48

or 30 + B = 48 or B = 12

and A + B = 30 or A = 30 - B = 30 - 12 = 18

A = 18 and B = 12