At a graduation ceremony, names were read at the rate of five names per minute. If the names had been read at the rate of seven names per minute, the ceremony would have taken 24 minutes less. How many names were read?

420 names were read

Step-by-step explanation:

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

Rate of names read per minute at the graduation ceremony = 5

2. If the names had been read at the rate of seven names per minute, the ceremony would have taken 24 minutes less. How many names were read?

x = Number of minutes it takes to read the names at the rate of seven names per minute

x + 24 = Number of minutes it takes to read the names at the rate of five names per minute

Solving for x:

5 * (x + 24) = 7x

5x + 120 = 7x

5x - 7x = -120 (Subtracting 120 and 7x at both sides)

-2x = -120

x = -120/-2

x = 60 ⇒ 7x = 420

420 names were read