Roy and elisa are buying tickets for the annual school concert. roy buys 6 adult tickets and 2 child tickets for a total of $66. elisa buys 5 adult tickets and 4 child tickets for a total of $62. determine the system of equations that can be used to find the cost of one adult ticket, a, and the cost of one child ticket, c.

The system of equations that could be used to find the cost of one adult ticket and one child ticket is:

On solving we get:

Cost of one adult ticket= $ 10

and cost of one child ticket= $ 3

a denote the cost of one adult ticket.

and c denote the cost of one child ticket.

Roy buys 6 adult tickets and 2 child tickets for a total of $66.

i.e. the equation that could be written is:

              6a+2c=66-----------(1)

and also Elisa buys 5 adult tickets and 4 child tickets for a total of $62.

This means that the equation  that is obtained from this information is:

                       5a+4c=62--------------(2)

Also, on solving the two equations by the method of elimination

we multiplying equation (1) by 2 and subtract both the equations we get:

            12a+4c=132

and        5a+4c=62

-----------------------------------

            7a=70

i.e.   a=10

and on putting the value of a in equation (1) we get:

    60+2c=66

i.e.  2c=66-60

i.e.   2c=6

i.e.  c=3

Hence, the cost of one adult ticket=$ 10

and cost of one child ticket= $ 3

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