Question

A-Lab assistant need to create a 900 ml mixture that is 4.5% hydroelectric acid. The assistant has solutions of 3% and 5.5% in supply at the lab. Using the variables x and y to represent the number of milliliters of 3% solution and the number of milliliters of the 5.5% solution respectively, determine a system of equation that describes the situation.Enter the equations below separated by a comma.How many milliliters of the 3% solution should be used?How many milliliters of the 5.5% solution should be used?

Answer 1

Let x and y to represent the number of milliliters of 3% solution and the number of milliliters of the 5.5% solution respectively. Given that the volume of the mixture is 900 ml, we have

x + y = 900

The mixture should contain 4.5% hydroelectric acid. Recall, percentage is expressed in terms of 100. The concentration of the mixture is

4.5/100 * 900 = 40.5

x should contain 3% of hydroelectric acid. The concentration of x is

3/100 * x = 0.03x

y should contain 5.5% of hydroelectric acid. The concentration of y is

5.5/100 * y = 0.055y

The equation representing the concentration would be

0.03x + 0.055y = 40.5

Thus, the required system of equations is

x + y = 900

0.03x + 0.055y = 40.5

From the first equation,

x = 900 - y

Substituting x = 900 - y into the second equation, we have

0.03(900 - y) + 0.055y = 40.5

27 - 0.03y + 0.055y = 40.5

- 0.03y + 0.055y = 40.5 - 27

0.025y = 13.5

y = 13.5/0.025

y = 540

x = 900 - y = 900 - 540

x = 360

360 ml of 3% solution and 540 ml of 5.5% solution should be used.