Question

You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total, how many dance tickets were sold?

Answer 1

11 dance tickets were sold. ( approx )

Explanation:

Let x represents the number of car wash tickets, y represents the number of silly string fight tickets and z represents number of dance tickets,

Total tickets = 380,

⇒ x + y + z = 380 -----(1),

The car wash tickets were $5 each, the silly string fight tickets were $3 each and the dance tickets were $10 each, also total cost is $1460,

⇒ 5x + 3y + 10z = 1460 ----(2)

Also, there are twice as many silly string tickets as car wash tickets,

⇒ y = 2x -----(3)

From equation (1) and (2),

x + 2x + z = 380 ⇒ 3x + z = 380 -----(4)

5x + 3(2x) + 10z = 1460 ⇒ 11x + 10z = 1460 ------(5)

For finding the value of z,

3 × equation (5) - 11 × equation (4),

We get,

30z - 11z = 4380 - 4180

19z = 200

z = 10.5263157895 ≈ 11

Hence, 11 dance tickets were sold.