Question

A new company, Voltaic Ventures, is researching longer-lasting, high-power car batteries. The company needs 16% Sulfuric Acid to run experiments with new battery technology. However, suppliers of sulfuric acid only deliver either 13% Sulfuric acid concentration or 18% Sulfuric acid concentration. How many gallons of each acid are needed to mix to produce 500 gallons of 16% acid?

Answer 1

To produce 500 gallons of 16% sulfuric acid, we use algebraic mixture equations to determine the precise amounts of 13% and 18% concentrations needed. By setting equations for total volume and desired concentration, we can solve for the two unknowns.

Step-by-step explanation:

To solve the problem of how many gallons of each sulfuric acid concentration are needed to produce 500 gallons of 16% acid, we can use the method of algebraic mixture equations.

Let's denote the amount of 13% sulfuric acid as x gallons and the amount of 18% sulfuric acid as y gallons. We have two unknowns and thus need two equations to solve the problem, based on the total volume and the desired concentration.

• The total volume of the mixture needs to equal 500 gallons: x + y = 500.
• The total amount of pure sulfuric acid in the mixture needs to result in a 16% concentration: 0.13x + 0.18y = 500 × 0.16.

First, we can solve for y in terms of x using the first equation: y = 500 - x. Then, we substitute this into the second equation:

0.13x + 0.18(500 - x) = 80,

and solving this equation gives us the values for x and y, indicating the exact gallons of each acid needed.