MATH: ALGEBRAIC EXPRESSIONS PORTFOLIO.
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.
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.
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?
A. Expression 1: T + 0.15T
Explanation: The cost of the ticket (T) plus 15% of the cost of the ticket (0.15T) gives the total cost including the amusement tax.
Expression 2: 1.15T
Explanation: The ticket cost (T) multiplied by 1.15 gives the total cost including the amusement tax.
B. Let's choose T = $12.50
Using expression 1, the total cost would be:
12.50 + 0.15(12.50) = 12.50 + 1.875 = $14.375
Conor's total cost, rounded to the nearest penny, would be $14.38.
C. To find a possible value of T, we need to determine a value where the total cost using Expression 1 (T + 0.15T) falls within the given range.
Let's try T = $12.50:
12.50 + 0.15(12.50) = 12.50 + 1.875 = $14.375
Since $14.38 is within the given range ($17.50 - $20), T = $12.50 could be a possible value.