Solve using a system of two equations in two unknowns.
-Dmitri needs 5 liters of a 7% solution of sulfuric acid for a research project in molecular biology. He has two unlimited supplies of sulfuric acid solution: 5% solution and 10% solution. How many
Liters of each solution should Dmitri use?
A) 5% solution: 3.5 L, 10% solution: 1.5 L
B)5% solution: 3 L, 10% solution: 2 L
C) 5% solution: 2.5 L, 10% solution: 2.5 L
D)5% solution: 2 L, 10% solution: 3 L

Question

Quizplus · Accepted Answer

Let x be the number of liters of the 5% solution and y be the number of liters of the 10% solution. Then we have the system of equations:

x + y = 5 (since Dmitri needs a total of 5 liters)
0.05x + 0.1y = 0.07(5) (since the final solution needs to be 7% sulfuric acid)

Simplifying the second equation, we get:

0.05x + 0.1y = 0.35

Multiplying both sides by 10 to eliminate decimals, we get:

5x + 10y = 35

Now we can use the first equation to solve for one of the variables in terms of the other. For example, solve for y:

y = 5 - x

Substitute this expression for y into the second equation to get:

5x + 10(5 - x) = 35

Simplify and solve for x:

5x + 50 - 10x = 35
-5x = -15
x = 3

So Dmitri needs 3 liters of the 5% solution. Substituting this back into the equation y = 5 - x, we get:

y = 5 - 3
y = 2

So Dmitri needs 2 liters of the 10% solution. Therefore, the best choice is B: 5% solution: 3 L, 10% solution: 2 L.

Solve Using a System of Two Equations in Two Unknowns