6 children’s tickets and 4 adult tickets cost $59.50 The total cost of 2 adult tickets and 3 senior tickets is $35.90 If each adult ticket costs 2 times as much

Question

6 children’s tickets and 4 adult tickets cost $59.50 The total cost of 2 adult tickets and 3 senior tickets is $35.90 If each adult ticket costs 2 times as much as each children’s ticket, what is the total cost of 4 senior tickets and 2 children’s tickets

Answer 1

C is Child ticket price

A is Adult ticket price

S is Senior ticket price

 

6C + 4A = 59.50

2A + 3S = 35.90 

A = 2C

 

Substitutes the third equation into the first equation:

 6C + 4(2C) = 59.50

 6C + 8C = 59.50

 14C = 59.50

  C = 59.50/14 = 4.25

 

Adult ticket is A= 2C = 2(4.25) = 8.50

 

Solving the second equation for S:

 

  3S = 35.90 - 2A 

 

  S = (35.90 - 2A)/3  = (35.90 - 2(8.50))/3

 

                                = (35.90 - 17)/3

 

                                = 18.90/3

 

                                = 6.30

 

Senior tickets cost $6.30

Children tickets cost 4.25

Adult tickets cost 8.50

 

6*4.25 + 4 * 8.50 = 59.50

2*8.50 + 3 *6.30 = 35.90

 

THese answers check out, so with confidence

we can say

 

4*6.30 + 2*4.25 = 33.70

 

shall be the price for 4 senior and 2 children tickets