A family of 6 is going to the fair. They have a coupon for $2.50 off each ticket. If they pay $96 for all of their tickets, and each ticket costs the same amount, how much does a ticket, t, cost without the coupon?

Question

How much is the family spending in all at the fair?

Answer 1

Let the original price of each ticket be \( t \) dollars. With the coupon, each ticket costs \( t - 2.50 \) dollars.

Since the family of 6 is buying 6 tickets, the total cost they paid with the coupon is given by:

\[ 6(t - 2.50) = 96 \]

Now, we can solve for \( t \):

1. Distribute the 6: \[ 6t - 15 = 96 \]

2. Add 15 to both sides: \[ 6t = 111 \]

3. Divide both sides by 6: \[ t = \frac{111}{6} = 18.5 \]

Thus, the cost of a ticket without the coupon is \( t = 18.50 \) dollars.

Next, to find out how much the family is spending in all at the fair without the coupon, we can multiply the original ticket price by the number of tickets:

\[ \text{Total cost without coupon} = 6t = 6 \times 18.50 = 111 \]

So, the family is spending a total of $111 at the fair before applying the coupon.