Answer:
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.
