Tickets to the basketball game are on sale for $1.50 off the regular price. Dea buys 6 tickets. If her total cost is $51, what is the regular price of each ticket? Write and solve an equation of the form p(x=q)=r. Then write a sentence to explain your answer.
Let's assume that the regular price of each ticket is 'p' dollars.
Since Dea bought 6 tickets, her total cost would be 6p dollars.
According to the given information, the tickets are on sale for $1.50 off, therefore the discounted price of each ticket would be (p - $1.50).
Hence, Dea's total cost can be expressed as follows:
6(p - $1.50) = $51.
To solve this equation:
6p - 9 = $51.
Adding 9 to both sides:
6p = $60.
Dividing both sides by 6:
p = $10.
Therefore, the regular price of each ticket is $10.
Sentence to explain the answer: The regular price of each ticket is $10 because when the tickets are on sale for $1.50 off, Dea's total cost is $51 for purchasing 6 tickets.
Let's say the regular price of each ticket is p dollars. The discounted price is p - $1.50.
Dea buys 6 tickets, so the total cost is 6 times the discounted price: 6(p - $1.50).
According to the problem, this total cost is $51, so we can write the equation as follows:
6(p - $1.50) = $51.
Simplifying the left side of the equation, we get 6p - $9 = $51.
Adding $9 to both sides, we have 6p = $60.
Finally, we divide both sides by 6: p = $10.
Therefore, the regular price of each ticket is $10.
To solve this problem, let's start by defining the variables:
Let p represent the regular price of each ticket.
Let x represent the number of tickets Dea buys.
Let q represent the discount of $1.50 off the regular price.
Let r represent the total cost.
According to the information given, the regular price of each ticket can be determined from the total cost and the discount.
We can write the equation representing this scenario as follows:
p(x) - q = r
In this case, Dea buys 6 tickets and her total cost is $51. Therefore, the equation becomes:
p(6) - 1.50 = 51
To find the regular price of each ticket, we need to isolate p in the equation. Let's solve for p:
p(6) - 1.50 = 51
6p - 1.50 = 51
6p = 51 + 1.50
6p = 52.50
p = 52.50/6
p ≈ 8.75
Therefore, the regular price of each ticket is approximately $8.75.
In summary, Dea's total cost for 6 tickets, including a discount of $1.50 per ticket, is $51. By solving the equation p(6) - 1.50 = 51, we find that the regular price of each ticket is approximately $8.75.