Question

Two families went to the event. The first family bought two children's tickets and one adult ticket and paid a total of 8.2 euros. The other family bought three children's tickets and two adult tickets and paid a total of 14.1 euros. Can you tell me how much one child costs and how much one adult ticket costs?

Answer 1

Explanation:

step a system of two equations c = child ticket a = adult ticket

eq 1) 2c + 1a = 8.2 multiply by 2

eq 2) 3c + 2a = 14.1

I will multiply eq 1 times TWO and subtract eq 2 from eq 1a)

eq 1a) 4c + 2a = 16.4

eq 2) 3c + 2a = 14.1

subtract (4c - 3c) + (2a -2a) = 16.4 - 14.1

c + 0 = 2.3 euros for one child ticket

Now find the adult ticket price, plug 2.3 for c into eq 1)

eq 1) 2c + 1a = 8.2

eq 1) 2(2.3) + 1a = 8.2 solve for a

4.6 + a = 8.2 substract 4.6 from both sides

a = 8.2 - 4.6

= 3.6 euros for one adult ticket

double check using eq 2) we know c and a values

eq 2) 3c + 2a = 14.1

eq 2) 3(2.3) + 2(3.6) = 14.1

6.9 + 7.2 = 14.1

14.1 = 14.1