Question

At a local fair, the admission fees are $1.50 for children, $3 for college students , and $5 for adults, On Saturday, 1500 tickets were sold and brought in $5500. The number of college student tickets sold were 100 less than the number of children's tickets sold. How many children's tickets were sold?​

Answer 1

• 240 children's tickets

Explanation:

Let the number of children be c, adults be a and students be s. We have:

• c + a + s = 1500
• 1.5c + 3s + 5a = 5500
• s = a - 100

Substitute a in the first and second equations:

• c + a + a - 100 = 1500 ⇒ c + 2a = 1600
• 1.5c + 3( a - 100) + 5a = 5500 ⇒ 1.5c + 8a = 5800

Eliminate c by doubling the second equation and subtracting triple of the first one:

• 16a - 6a = 2(5800) - 3(1600)
• 10a = 6800
• a = 680

Then find s and c:

• s = 680 - 100 = 580
• c = 1500 - (680 + 580) = 240

Answer: 240 children's tickets were sold