Question 1:

Question

Connor is going to the movie theater. A ticket to a movie costs t dolllars, and there is a 15% amusement tax on each ticket.

A. Connor buys a ticket to see a movie. Write 2 expressions in term of t showing his total cost.+2

B. Choose a value for t is $11.50. Use one of the expressions u wrote n part a to find Connors total cost, rounded to the nearest penny. Show work +2

C. Suppose Connors total cost to see the movie is $ 18.40 what is the value of t to make that possible? +2

Question 2:

Winona and Takoda are shopping for a present for their mother. The chart shows several possible presents. There is no sales tax in the state where they live.

PRESENT
Power tools
Water
Jewelry

COST ( $ )
d
d + 15

d - 5

DISCOUNT ( % )

15%

25%

10%

TOTAL PAID

( +2 )
( +2 )
( +2 )

A. Write two expressions in term of d to show how much Winona and Takoda would pay in total if they but their mother the set of power tools.

B. What present does the expression 0.90 ( d -5 ) refer to?

C. Use the value d=$50. Calculate the TOTAL PAID ( +6pts see above ) Column of each of the possible presents for the value of $50. Then star or circle the most economical or cheapest ( +1 )

Answer 1

Question 1

A.

To determine Connor's total cost when he buys a ticket to see a movie, we have to account for the ticket price and the amusement tax.

1. Cost of the ticket alone: \( t \)
2. Amusement tax (15% of ticket price): \( 0.15t \)

Therefore, the total cost (TC) will be the sum of the ticket price and the tax:

\[ \text{Total Cost} = t + 0.15t \]

This can also be expressed as:

\[ \text{Total Cost} = 1.15t \]

B.

Choosing a value for \( t \) as $11.50, we can calculate Connor's total cost using the expression we derived:

\[ \text{Total Cost} = 1.15 \times 11.50 \]

Calculating this:

\[ \text{Total Cost} = 13.225 \]

Rounding to the nearest penny, Connor's total cost is:

\[ \text{Total Cost} \approx 13.23 \]

C.

If Connor's total cost to see the movie is $18.40, we can use our total cost expression to find the value of \( t \):

\[ 1.15t = 18.40 \]

Now, isolate \( t \):

\[ t = \frac{18.40}{1.15} \]

Calculating this gives:

\[ t = 16.00 \]

So, the value of \( t \) to make that total cost possible is $16.00.

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Question 2

A.

For the power tools, we need to find two expressions in terms of \( d \):

1. The cost of the power tools before the discount is \( d \).
2. The discount is 15% of \( d \), calculated as \( 0.15d \).

The total paid after the discount can be expressed as:

\[ \text{Total Paid} = d - 0.15d = 0.85d \]

Thus, an expression in terms of \( d \) for the total paid for power tools is:

\[ \text{Total Paid} = 0.85d \]

B.

The expression \( 0.90(d - 5) \) refers to the jewelry, since the cost of the jewelry before discount is \( d - 5 \) and the discount is 10%.

C.

Given \( d = 50 \), we will calculate the total paid for each present:

1. Power Tools: \[ \text{Total Paid} = 0.85 \times 50 = 42.50 \]

2. Water: The cost is \( d + 15 \): \[ \text{Cost} = 50 + 15 = 65 \] Now applying the 25% discount: \[ \text{Total Paid} = 0.75 \times 65 = 48.75 \]

3. Jewelry: The cost is \( d - 5 \): \[ \text{Cost} = 50 - 5 = 45 \] Now applying the 10% discount: \[ \text{Total Paid} = 0.90 \times 45 = 40.50 \]

Now we summarize the total paid for each present:

• Power Tools: $42.50
• Water: $48.75
• Jewelry: $40.50

To identify the most economical or cheapest option, we clearly see that the Jewelry at $40.50 is the cheapest present.

Final note: Circle or star the Jewelry in the results list as the most economical option.