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

$\ 17000 \cdot (1 - \dfrac{1}{4}) = \ 12750$.

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.