Owen is making lemonade from concentrate. The number of quarts of water he needs is 4 times the number of quarts of concentrate. He wants to make 100 quarts of lemonade.

Let c represent the number of quarts of concentrate, and let w represent the number of quarts of water Owen will use. Which of the following systems of equations models this situation?

The system of equation that models the situation is:

w = 4c

w + c = 100

And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.

Step-by-step explanation:

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

Owen wants to make 100 quarts of lemonade

Number of quarts of water 4 times the number of quarts of concentrate

2. Which of the following systems of equations models this situation?

c = number of quarts of concentrate

w = number of quarts of water

Like the alternatives of systems of equations that model the situation were not given, let's write them by ourselves, this way:

w = 4c (Number of quarts of water 4 times the number of quarts of concentrate)

w + c = 100 (Owen wants to make 100 quarts of lemonade)

Now, let's solve for c and w, this way:

w = 100 - c

Substituting w in the first equation, we have:

100 - c = 4c

100 = 5c

c = 20 ⇒ 4c = 20 * 4 = 80

w = 4 * 20

w = 80

The system of equation that models the situation is:

w = 4c

w + c = 100

And c = 20 quarts, 4c = 80 quarts and w = 80 quarts.