Question

Beth wrote a system of equations to determine when a referee will earn the same salary working the East Conference and West Conference games. y = 40x − 25 and y = 35x − 5 (x = total games and y = amount earned) Beth determined that at 135 games, the referee would earn the same salary for each conference game. Is she correct?

Answer 1

Beth is incorrect; the referee will earn the same salary after working 4 games, not 135 games.

Step-by-step explanation:

To verify if Beth is correct in determining that at 135 games, the referee would earn the same salary for East Conference and West Conference games, we need to solve the system of equations she provided:

• y = 40x - 25 (East Conference)
• y = 35x - 5 (West Conference)

By setting these two equations equal to each other, we can find the value of x (number of games) where the referee's earnings will be identical:

40x - 25 = 35x - 5

To solve for x, we'll combine like terms:

40x - 35x = -5 + 25

5x = 20

Now, divide both sides by 5 to isolate x:

x = 4

This result indicates that the referee will earn the same amount for both conferences after working 4 games, not 135 games. Therefore, Beth's calculation is incorrect.

Answer 2

She is incorrect

Step-by-step explanation:

Step 1: substitute

135 into x in both equations

Step 2: Solve the equations. Once you do this you will get y = 5375 for the first one and y = 4720 for the second one, therefore she is incorrect