Question

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.

Answer 1

The system of equations is.....

`3a+c=33\\ 5a+4c=62`

Explanation:

The cost of one adult ticket is 'a' and the cost of one child ticket is 'c'

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

So, the cost of 6 adult tickets
`=6a` dollar and the cost of 2 child tickets
`=2c` dollar.

Thus, the first equation will be:
`6a+2c=66` or
`3a+c=33` (Dividing both sides by 2)

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

So, the cost of 5 adult tickets
`=5a` dollar and the cost of 4 child tickets
`=4c` dollar.

Thus, the second equation will be:
`5a+4c=62`

So, the system of equations that can be used to find the cost of one adult ticket and the cost of one child ticket will be.....

`3a+c=33\\ 5a+4c=62`

Answer 2

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

`6a+2c=66\\\\and\\\\5a+4c=62`

On solving we get:

Cost of one adult ticket= $ 10

and cost of one child ticket= $ 3

Explanation:

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