Question

I need help with coming up with equation

Answer 1

Let's call a child's ticket
`c` and an adult's ticket
`a`. From this, we can say:

`c + a = 116`,

since 116 tickets are sold in total.

Now, we are going to need to find another equation (the problem asks us to solve a systems of equations). This time, we are not going to base the equation on ticket quantity, but rather ticket price. We know that an adult's ticket is $17,000, and a child's ticket is thus

`\$17000 \cdot (1 - (1)/(4)) = \$12750`.

Given these values, we can say:

`17000a + 12750c = 1653250`,

since each adult ticket
`a` costs 17,000 and each child's ticket
`c` costs 12,750, and these costs sum to 1,653,250.

Now, we have two equations:

`17000a + 12750c = 1653250`

`c + a = 116`

Let's solve:

`17000a + 12750c = 1653250`

`a = 116 - c`

• Find
  `a` on its own, which will allow us to substitute it into the first equation

`17000(116 - c) + 12750a = 1653250`

• Substitute in
  `116 - c` for
  `a`

`1972000 - 17000c + 12750c = 1653250`

• Apply the Distributive Property

`1972000 - 4250c = 1653250`

• Combine like terms

`4250c = 318750`

• Subtract 1972000 from both sides of the equation and multiply both sides by -1

`c = 75`

We have now found that 75 child's tickets were sold. Thus,

`75 + a = 116 \Rightarrow a = 116 - 75 = 41`,

41 adult tickets were sold as well.

In sum, 41 adult tickets were sold along with 75 child tickets.