Question

The entrance fees to a theme park are $10.00 for adults and $6.00 for children. On a slow day there are 20 people who pay entrance fees for a total of $164.00 solve the simultaneous equations to work at the number of adults and numbers of children?

Answer 1

See a solution process below:

Explanation:

First, let's call the number of adults who attended: `a`

And the number of children who attended: `c`

We know there were 20 people total who attended so we can write our first equation as:

`a + c = 20`

We know they paid $164.00# so we can write our second equation as:

`$10.00a + $6.00c = $164.00`

Step 1: Solve the first equation for `a`:

`a + c - color(red)(c) = 20 - color(red)(c)`

`a + 0 = 20 - c`

`a = 20 - c`

Step 2: Substitute `(20 - c)` for `a` in the second equation and solve for `c`:

`$10.00a + $6.00c = $164.00` becomes:

`$10.00(20 - c) + $6.00c = $164.00`

`($10.00 xx 20) - ($10.00 xx c) + $6.00c = $164.00`

`$200.00 - $10.00c + $6.00c = $164.00`

`$200.00 + (-$10.00 + $6.00)c = $164.00`

`$200.00 + (-$4.00)c = $164.00`

`$200.00 - $4.00c = $164.00`

`$200.00 - color(red)($200.00) - $4.00c = $164.00 - color(red)($200.00)`

`0 - $4.00c = -$36.00`

`-$4.00c = -$36.00`

`(-$4.00c)/(color(red)(-)color(red)($)color(red)(4.00)) = (-$36.00)/(color(red)(-)color(red)($)color(red)(4.00))`

`(color(red)(cancel(color(black)(-$4.00)))c)/cancel(color(red)(-)color(red)($)color(red)(4.00)) = (-color(red)(cancel(color(black)($)))36.00)/(color(red)(-)cancel(color(red)($))color(red)(4.00))`

`c = (-36.00)/(color(red)(-)color(red)(4.00))`

`c = 9`

Step 3: Substitute `9` for `c` in the solution to the first equation at the end of Step 1 and calculate `a`:

`a = 20 - c` becomes:

`a = 20 - 9`

`a = 11`

11 adults and 9 children attended the theme park.