Answer:
11 dance tickets were sold. ( approx )
Step-by-step 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.
