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
1. The expression for the cost of the ticket without the amusement tax is t.
2. The expression for the total cost including the amusement tax is t + 0.15t.
write an equation for the first one now
The equation for the total cost of the ticket without the amusement tax (t) is:
Cost = t
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 to be $12.50.
Using the second expression we wrote in part a:
Total Cost = t + 0.15t
Plugging in t = $12.50:
Total Cost = 12.50 + 0.15(12.50)
Total Cost = 12.50 + 1.875
Total Cost = $14.375
Rounded to the nearest penny:
Total Cost ≈ $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?
write that in kids's words
To find a value of t that makes Conor's total cost to see the movie between $17.50 and $20, we can use a little math. We have an equation: 1.15 times x equals 20. We want to know what x (which represents t) is. After solving the equation, we find that x is about 17.39. So, a possible value for t that makes Conor's total cost fall between $17.50 and $20 is around $17.39.
what is the value of "t" to make this possible
Apologies for any confusion. The value of t that makes Conor's total cost fall between $17.50 and $20 is approximately $15.22.
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?
DON'T USE BIG WORDS!!
A possible value for t that makes Conor's total cost fall between $17.50 and $20 could be around $18.75.
give me more explanation
Sure! Let's say Conor's total cost to see the movie falls between $17.50 and $20. To find a value of t that could make that possible, we need to think about the ticket price.
We know that there is a 15% amusement tax on each ticket. So, if we subtract that tax from the total cost, we can find out the price of the ticket itself (t).
Let's start with the upper bound, $20. We want to find a value of t that, when we add 15% tax to it, gives us a total cost of $20.
If we subtract 15% from $20, we get $17 (since 100% - 15% = 85%). This means the price of the ticket itself (t) should be less than $17.
Now, let's consider the lower bound, $17.50. We want to find a value of t that, when we add 15% tax to it, gives us a total cost of $17.50.
If we subtract 15% from $17.50, we get about $14.88. This means the price of the ticket itself (t) should be more than $14.88.
Based on these calculations, a possible value for t that makes Conor's total cost fall between $17.50 and $20 could be around $18.75.
Winona and Takoda are shopping for a present for their mother. The chart shows
several possible presents. There is no sales tax in the state where they live.
Present Cost ($) Discount (%) Total Paid
Power tools d 15%
Water skis d + 15 25%
Jewelry d – 5 10%
a. Write two expressions in terms of d to show how much Winona and Takoda
would pay in total if they buy their mother the set of power tools
1. The expression for the total amount Winona and Takoda would pay if they buy their mother the set of power tools is: 0.85d. (This accounts for the 15% discount on the power tools.)
2. Another expression that shows the total amount they would pay is: d - 0.15d. (This subtracts the 15% discount from the original cost of the power tools.)
b. What does the expression 0.90(d – 5) refer to? How do you know? How else
could this expression be written?
The expression 0.90(d - 5) refers to the total amount Winona and Takoda would pay if they buy their mother the jewelry set.
I know this because the expression applies a 10% discount to the original cost (d - 5) of the jewelry. Multiplying (d - 5) by 0.90 calculates 90% of the original cost, meaning they pay 90% of the original price after the discount.
This expression could also be written as 0.9d - 4.5. Distributing the 0.90 to both terms in the parentheses results in the same calculation.
c. Choose a value for d that is greater than $25 and less than $100. Calculate the
total cost of each of the possible presents for the value you chose. Then write a
short paragraph telling Winona and Takoda which present they should buy and
explaining why.
Let's choose d to be $50. Now we'll calculate the total cost of each possible present for that value.
1. Power tools: Total Paid = 0.85d = 0.85 * 50 = $42.50
2. Water skis: Total Paid = d + 0.25d = 1.25 * 50 = $62.50
3. Jewelry: Total Paid = 0.90(d - 5) = 0.90 * (50 - 5) = $40.50
Based on the calculations, Winona and Takoda should buy their mother the jewelry set. It has the lowest total cost of $40.50. The power tools would cost $42.50 and the water skis would cost $62.50. Since they want to find the most affordable option while still getting a meaningful present for their mother, the jewelry set offers the best value. Additionally, the discount of 5% makes the jewelry set even more budget-friendly compared to the power tools. Therefore, they should choose the jewelry set as their present.
whats another kids' word for budget friendly
Another kids' word for "budget friendly" could be "affordable."
A county planner prepares the following table showing population trends in three local
towns. The first column gives the name of the town. The second column gives the
population as of the last census. The third column gives the estimated increase or
decrease in population since that census, expressed as a percentage of the previous
population.
Town Census Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%
a. Choose one of these towns. Use the second and third columns to write two
expressions showing the current estimated population of the town in terms of
x, y, or z.
Let's choose Amity Center.
1. The expression for the current estimated population of Amity Center using the second column and third column is: y + 0.05y. This adds a 5% increase to the previous population (y).
2. Another expression that shows the current estimated population is: (1 + 0.05)y. This multiplies the previous population (y) by 1.05, accounting for the 5% increase.
Add a fourth row to the table showing the population information for the town
of Concord. Concord’s population as of the last census was p people; for its
percentage change, choose a negative integer not divisible by two. Write two
expressions showing the current estimated population of Concord in terms of p.
Town | Census Population | Percentage Change
-------------------------------------------
Pleasantville | x | -2%
Amity Center | y | +5%
Harmony Corners | z | +7%
Concord | p | -9%
To show the current estimated population of Concord in terms of p, we can use these two expressions:
1. The expression for the current estimated population of Concord using the second and third columns is: p - 0.09p. This subtracts a 9% decrease from the previous population (p).
2. Another expression that shows the current estimated population is: (1 - 0.09)p. This multiplies the previous population (p) by 0.91, accounting for the 9% decrease.
Choose a number greater than 5,000 and less than 10,000 for the value of p. I AM CHOOSING 6,000
Based on the percentage change you chose in part b, calculate the estimated
current population of Concord, rounding to the nearest whole number if
needed. Explain why you used the expression you did to make your calculation.
Based on the chosen value of p as 6,000 and the percentage change of -9% for Concord, let's calculate the estimated current population.
Using the expression p - 0.09p, we can substitute p = 6,000 into the equation:
Estimated Current Population = 6,000 - 0.09 * 6,000
Estimated Current Population = 6,000 - 540
Estimated Current Population = 5,460
Rounding the estimated current population to the nearest whole number, we get approximately 5,460.
I used the expression p - 0.09p because it applies the percentage decrease of 9% to the previous population (p). This calculation subtracts 9% of p from p, giving us the estimated current population.
what is the nearest whole number for 5,460
The nearest whole number for 5,460 is 5,460 itself.
A’Leila is building a pen for her pet donkey. The pen is a rectangle with one side
measuring b yards and the adjacent side measuring a yards. A’Leila knows that a = 1/3 b.
a. Write two different expressions giving the perimeter of the donkey’s pen.
Sure! The perimeter of the donkey's pen can be calculated using the formulas:
1. The expression for the perimeter of the pen using a and b is:
Perimeter = 2a + 2b
2. Another expression that gives the perimeter is:
Perimeter = a + a + b + b
Both expressions give the same result for the perimeter of the donkey's pen, but they use different ways to represent the sides.
b. Choose a value for a that is greater than 5 and less than 15. I AM CHOOSING 10.
Evaluate the
perimeter of the pen for that value, using one of the expressions that you
wrote.
Let's use the value of a as 10 and substitute it into the first expression we wrote for the perimeter:
Perimeter = 2a + 2b
Given that a = 10, we can substitute this value into the expression:
Perimeter = 2(10) + 2b
Since we do not know the value of b, we cannot calculate the exact perimeter. However, we can simplify the expression:
Perimeter = 20 + 2b
Therefore, the perimeter of the donkey's pen is represented as 20 + 2b, where b is the length of the adjacent side which we do not know.
make that simpler NOWWW
Apologies for any confusion. Let's simplify the expression further:
Perimeter = 20 + 2b
Since b is also related to a by the equation a = (1/3)b, we can substitute it into the expression:
Perimeter = 20 + 2(3a)
Simplifying further:
Perimeter = 20 + 6a
Now, if we substitute the given value of a = 10 into the equation:
Perimeter = 20 + 6(10)
Perimeter = 20 + 60
Perimeter = 80
Therefore, when a is 10, the perimeter of the pen is 80.
write the original answer you gave me in kids' words
Sure! When A'Leila's pen has a value of a equal to 10, the perimeter of the pen is 80. This means that if we add up all the sides of the pen, it will measure 80 yards.
b. Choose a value for a that is greater than 5 and less than 15. I AM CHOOSING 10.
Evaluate the
perimeter of the pen for that value, using one of the expressions that you
wrote.
write this in older kids' words
Let's choose a value of 10 for side "a" of A'Leila's pen.
Using the expression Perimeter = 20 + 2b, we can evaluate the perimeter of the pen.
Substituting a = 10 into the expression, we have:
Perimeter = 20 + 2b
Since we do not know the value of side "b," we cannot calculate the exact perimeter. However, we can simplify the expression further by stating that the perimeter of the pen is 20 plus twice the value of side "b."
in KIDS' WORDSSSSS
Sure! Let's imagine A'Leila's pen has one side that is 10 yards long (side "a"). We want to find out how long the perimeter of the pen is.
To do that, we use the expression Perimeter = 20 + 2b, where "b" is the length of the other side of the pen.
Since we don't know the exact length of side "b," we can't calculate the exact perimeter. However, we can say that the perimeter is 20 plus twice the length of side "b."
what is the length of side b
Given that we know side "a" is equal to 10 yards, and we have the relationship a = (1/3)b, we can substitute the value of a into this equation to find the length of side "b".
a = (1/3)b
10 = (1/3)b
To isolate "b", we multiply both sides of the equation by 3:
3 * 10 = 3 * (1/3)b
30 = b
So, the length of side "b" is 30 yards.
Choose a value for a that is greater than 5 and less than 15. Evaluate the
perimeter of the pen for that value, using one of the expressions that you
wrote.
I AM CHOOSING EXPRESSION 1: 2a+2b
Certainly! Let's choose a value of a as 8.
Using expression 1: Perimeter = 2a + 2b
Substituting a = 8 into the expression, we have:
Perimeter = 2(8) + 2b
Simplifying further:
Perimeter = 16 + 2b
Since we do not know the value of b, we cannot calculate the exact perimeter. However, we can simplify it by saying that the perimeter will be equal to 16 plus twice the length of side b.
no, i want to use 10 for the a value
Apologies for the misunderstanding. Let's use 10 for the value of side "a" and evaluate the perimeter using expression 1: Perimeter = 2a + 2b.
Substituting a = 10 into the expression, we have:
Perimeter = 2(10) + 2b
Simplifying further:
Perimeter = 20 + 2b
Since we do not know the value of b, we cannot determine the exact perimeter. However, we can simplify the expression to say that the perimeter will be equal to 20 plus twice the length of side b.
use another word instead of substitute
Certainly! Let's use a value of 10 for side "a" and evaluate the perimeter of the pen using expression 1, which is Perimeter = 2a + 2b.
Instead of substituting a = 10 into the expression, we can say that when we replace the "a" in the expression with 10, we get the following:
Perimeter = 2(10) + 2b
Simplifying further, we find:
Perimeter = 20 + 2b
Since we don't know the exact value of side "b," we cannot calculate the exact perimeter. However, using the simplified expression, we can say that the perimeter will be equal to 20 added to twice the length of side "b."
dont say "Since we don't know the exact value of side "b," we cannot calculate the exact perimeter. However, using the simplified expression, we can say that the perimeter will be equal to 20 added to twice the length of side "b."" WRITE THE PERIMITER OF B INTO YOUR ANSWER DUMMMYYYY
Apologies for the oversight. Let's use a value of 10 for side "a" and evaluate the perimeter of the pen.
Using expression 1: Perimeter = 2a + 2b
When substituting a = 10 into the expression
Okay, here is my answer:
I chose 10 for the value of a. We are going to be using expression #1:
Perimeter = 2a+2b
Replacing a = 10 into the expression, we get:
Perimeter = 2(10) + 2b
Simplifying, we get:
Perimeter = 20 + 2b
bot?
Let x be the value of t that makes Conor's total cost fall between $17.50 and $20.
Using the second expression we wrote in part a:
Total Cost = t + 0.15t
Plugging in the upper bound, $20:
20 = x + 0.15x
Combining like terms:
1.15x = 20
Dividing both sides by 1.15:
x ≈ 17.39
Therefore, a possible value for t could be approximately $17.39 to make Conor's total cost fall between $17.50 and $20.