Question

A scientist needs 10 L of a solution that is 60% acid. She has a 50% acid solution and a 90% acid solution she can mix together to make the 60% solution.

Let x represent the number of liters of the 50% solution.
Let y represent the number of liters of the 90% solution.
Which equation represents the total liters of acid that are needed?
Question 3 options:
x + y = 6
x + y = 10
0.5x + 0.9y = 6
0.5x + 0.9y = 10

Answer 1

The correct equation that represents the total liters of acid needed is 0.5x + 0.9y = 6, where x is liters of the 50% acid solution and y is liters of the 90% acid solution.

Step-by-step explanation:

The question involves the creation of a new solution by mixing two solutions of different acid concentrations. We are trying to find an equation that represents the total liters of acid needed for a final solution.

Using the given information, let x be the liters of the 50% acid solution and y be the liters of the 90% acid solution. Since the scientist needs 10 L of a 60% acid solution, the total amount of pure acid in the final solution needs to be 60% of 10 L, which is 6 L (60/100 * 10 = 6). Therefore, the amount of acid from the first solution plus the amount from the second solution needs to equal 6 L. The equation 0.5x + 0.9y = 6 correctly represents this, since 0.5x is the amount of acid from the 50% solution and 0.9y is the amount of acid from the 90% solution.

Answer 2

The equations system is:

x + y = 10

0.5x + 0.9y = 6

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Liters of 60% acid solution needed = 10

x = Number of liters of the 50% solution

y = Number of liters of the 90% solution

2. Which equation represents the total liters of acid that are needed?

There are two equations needed:

The first one related to the total liters needed, 10 in this case:

x + y = 10

The second one related to the acid concentration of the 10 liters:

0.5x + 0.9y = 10 * 0.6

0.5x + 0.9y = 6

The equations system is:

x + y = 10

0.5x + 0.9y = 6

Solving for x and y in the 2nd equation, we have:

0.5 (10 - y) + 0.9y = 6

5 - 0.5y + 0.9y = 6

0.4y = 6 - 5

0.4y = 1

y = 1/0.4 = 2.5 ⇒ x = 7.5 (10 - 2.5)

The scientist can mix 7.5 liters of the 50% acid solution and 2.5 liters of the 90% acid solution to get the 10 liters of the 60% acid solution.