I need help for my math homework

Question

at the end of the 2007-2008 football season, 38 super bowl games had been played with the two current football leagues, The AFC and the NFC. The NfC won two more games than the AFC. how many games did each conference win

Answer 1

To answer this question, we need to consider what is known and what is currently unknown.

Known: 38 total Super Bowls

Unknown: the number won by each of two conferences

These unknowns can be represented as with variables to serve as placeholders until their values are known. I will use a and n. To have the total, a is being added to n.

a + n = 38

The NFC has won two more games than the AFC. This means that if we add two to the number of games won by the AFC then it should equal the number of games won by the NFC.

n = a + 2

The system of equations derived is the following:

a + n = 38

n = a + 2

Since a variable is already isolated, substitution would be an excellent method for finding the solution. Plug "a+2" in for n.

a + (a+2) = 38

Combine like terms.

a + (a+2) = 38

a + a + 2 = 38

2a + 2 = 38

Solve the two-step equation. 1) add or subtract 2) multiply or divide

Subtract the two from both sides.

2a = 36

Divide by two on both sides.

a = 18

The AFC has won 18 games. Any of the two equations in the system can be chosen to find the next solution. In a system, a solution is only a true solution if it is true for both equations. I will use the second one as it is already set equal to n.

n = a + 2

n = 18 + 2

n = 20

The NFC won 20 games.