Question

Mary is buying tickets for a movie??? Each adult ticket costs $9 - Each child ticket costs $5 - Mary spends $110 on tickets - Mary buys 14 total tickets

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Answer 1

`4` child tickets and `10` adult tickets.

Explanation:

We will make two equations out of the given information.

I am going to give `"adult ticket"` the variable `a` and `"child ticket"` the variable `c`.

The first equation we can make is from this sentence: "Mary spends `$110` on tickets". We know that the `a` costs `$9` and `c` costs `$5` so this is our equation:

`9a + 5c = 110`

The second one says that "Mary buys 14 total tickets". Since those 14 tickets are a combination of adult tickets and child tickets, the equation is:

`a + c = 14`

We'll rearrange it so that we are able to subsitute it into the other equation:

`a + c = 14`

`a = 14 -c`

Now substitute and solve:

`9a + 5c = 110`

`9(14 - c) + 5c = 110`

`126 - 9c + 5c = 110`

`126 - 4c = 110`

`-4c = -16`

`-c = -4`

Since they're both negative, we can multiply them by `-1` to make them both positive because
`"negative" xx "negative" = "positive"`

`-c xx -1 = -4 xx -1`

`c = 4`

Now put `c` into one of the equations to solve for `a`. Any equation will produce the right value, I'll just use this one:

`a = 14 -c`

`a = 14 - (4)`

`a = 10`

Mary bought `10` adult tickets and `4` child tickets.