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? youre trying to find the original cost of 1 ticket for the fair, without the coupon. write an equation that can help you solve for t, the original cost of 1 ticket. 96 t - 2.50t - 2.50t - 2.50t - 2.50t - 2.50t - 2.50 1 ticket

Explanation:

Step1: Define total discounted cost

There are 6 tickets, each costing $t-2.50$, so total cost is $6(t-2.50)$. This equals $96$.
<Expression>
$$6(t - 2.50) = 96$$
</Expression>

Step2: Solve for t: divide both sides by 6

Divide total cost by number of tickets to get per-ticket discounted price.
<Expression>
$$t - 2.50 = \frac{96}{6}$$
$$t - 2.50 = 16$$
</Expression>

Step3: Isolate t: add 2.50 to both sides

Add the coupon value back to find original price.
<Expression>
$$t = 16 + 2.50$$
$$t = 18.50$$
</Expression>

Answer:

Equation: $6(t - 2.50) = 96$
Original ticket cost: $\$18.50$