Conor is going to the movie theater. A ticket to a movie costs t dollars, and there is a
15% amusement tax on each ticket.
a. Conor buys a ticket to see a movie. Write two expressions in terms of t
showing his total cost
e
One expression to show Conor's total cost would be t + 0.15t, which represents the cost of the ticket plus the 15% amusement tax.
Another expression could be 1.15t, which represents the total cost after adding the 15% amusement tax to the ticket price.
make it into a math eqaution
The math equation representing Conor's total cost can be written as:
Total cost = ticket price (t) + amusement tax (0.15t)
or
Total cost = ticket price (t) + (15/100)t
or
Total cost = ticket price (t) + 0.15t
b. Choose a value for t greater than $12 and less than $13. Use one of the
expressions you wrote in part a to find Conor’s total cost, rounded to the
nearest penny. Show your work.
Let's choose t = $12.50 as our value for the ticket price.
Using the expression Total cost = t + 0.15t, we can calculate Conor's total cost:
Total cost = 12.50 + 0.15 * 12.50
= 12.50 + 1.875
= 14.375
Rounded to the nearest penny, Conor's total cost is $14.38.
c. Suppose that Conor’s total cost to see the movie is greater than $17.50 and
less than $20. What could be a value of t to make that possible
To find a suitable value of t that would make Conor's total cost fall between $17.50 and $20, we can use the equation Total cost = t + 0.15t.
Let's start by setting up an inequality:
17.50 < t + 0.15t < 20
To simplify the inequality, we can combine like terms:
17.50 < 1.15t < 20
Next, we can divide all sides of the inequality by 1.15 to isolate t:
17.50 / 1.15 < t < 20 / 1.15
This simplifies to:
15.2174 < t < 17.3913
Based on this range, a suitable value for t that would make Conor's total cost fall between $17.50 and $20 would be any value within this range. For example, t = $16.00 would be a possible value.
make it easy
To find a value of t that would make Conor's total cost fall between $17.50 and $20, we can set up the inequality:
$t + 0.15t > 17.50$ and $t + 0.15t < 20$
We can simplify this to:
$1.15t > 17.50$ and $1.15t < 20$
Next, we divide both sides of the inequalities by 1.15:
$t > \frac{17.50}{1.15}$ and $t < \frac{20}{1.15}$
This simplifies to:
$t > 15.22$ and $t < 17.39$
Based on this range, a suitable value for t that would make Conor's total cost fall between $17.50 and $20 would be any value within this range. For example, t = $16.00 would be a possible value.