Question

Asha has $100 on a movie theatergift card. Each time she buys a ticketto a movie it costs her $8.75. Writean equation that Asha can use to findX, the number of tickets she can buyif she wants to keep a $15 balance onthe gift card.

Answer 1

We can write an equation for the balance of the gift card.

We know that if she doesn't buy any ticket (x = 0), the balance will be $100, which is the initial balance.

Each increase in x, is a decrease of 8.75 for the balance. This represents the slope of the equation, as there is not other term.

Then, we can write the equation as:

`y=100-8.75x`

If she wants to know how many tickets she can buy to have a $15 balance (y = 15), we can use the equation as:

`\begin{gathered} y=15 \\ 100-8.75x=15 \\ 100-15=8.75x \\ 85=8.75x \\ x=(85)/(8.75) \\ x\approx9.71 \end{gathered}`

She can buy up to 9 tickets (if she buys 10 tickets, she will have less than $15).

Answer:

The equation is y = 100 - 8.75x.

X = 9 tickets for a balance of $15.