Question
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?
How much is the family spending in all at the fair?
How much is the family spending in all at the fair?
Answers
GPT-4o mini
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.
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.