Question

Please help ASAP. I don’t understand the question.

Answer 1

Senior citizen ticket: $9

Child ticket: $13

Explanation:

This can be solved by creating a system of equations:

`f(x)=7x+5y=128`

and

`g(x)=8x+10y=202`

where x is the cost of a senior citizen ticket and y is the cost of a child ticket.

Solve equation 2 for 5y:

`8x+10y=202\\10y=202-8x\\(10y)/(x)=(202-8x)/(2)\\5y=101-4x`

Substitute (101-4x) for 5y in equation 1:

`7x+(101-4x)=128\\3x+101=128\\(3x+101)-101=(128)-101\\3x=27\\(3x)/(3)=(27)/(3)\\x=9`

Substitute 9 for x in equation 2:

`8(9)+10y=202\\72+10y=202\\(72+10y)-72=(202)-72\\10y=130\\(10y)/(10)=(130)/(10)\\y=13`

A senior citizen ticket costs $9 and a child's ticket costs $13.

To check these values, insert them into the equations:

`128=7(9)+5(13)\\128=63+65\\128=128`

and

`202=8(9)+10(13)\\202=72+130\\202=202`