math

A school sells tickets for a show, (a) adult tickets and (c) child tickets.

1) each adult ticket costs $8 and each child ticket costs $5. the total takings are 2300.
Write an equation to represent this information.

2) solve algebraically the simultaneous equations to find the values of a and c.

i think the first one is 8a + 5c = 2300 but i'm not sure about the second one.

please help

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  1. The question as it is will allow you to formulate one equation which you did correctly.

    It is normal that the question also tells you how many tickets have been sold in all. The total number of tickets sold should range between 289 to 460. This way, you can formulate a second equation of the form
    a+c=N where 289≤N≤460

    If this information is not given, there are many possible solutions.

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  2. forgot to write it, the school sells 370 tickets

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  3. So the second equation would be
    a + c = 370 ....(2)
    and the first equation is as you had it:
    8a + 5c = 2300 ....(1)

    You can solve it using substitution, namely, using (2),
    a=370-c
    and substitute a into equation (1) to get
    8(370-c)+5c = 2300

    Solve for c and subsequently for a.

    Don't forget to put back your answers into equations (1) and (2) for a check.

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