Question

The $120 cost of the field trip was to be shared equally by all those attending. Since 8 less students attended than were expected, the price per person increased by $0.50. How many students went on the field trip?

Answer 1

• 52

Explanation:

Let the number of students be x

Initial share was:

• 120/x

With the less students the share is:

• 120 /(x - 8) = 120/x + 0.5

Solve for x:

• 120 /(x - 8) = 120/x + 0.5
• 120x = 120(x - 8) + 0.5x(x - 8)
• 120x = 120x - 960 + 0.5x² - 4x
• 0.5x² - 4x - 960 = 0
• x² - 8x - 1920 = 0
• x² - 8x + 16 = 1936
• (x - 8)² = 1936
• x - 8 = √1936
• x - 8 = 44
• x = 52

52 students