Conor buys a ticket to see a movie. Write two expressions in terms of t
showing his total cost
Let's assume the cost of the ticket is $x.
First expression: If Conor buys only one ticket, his total cost would be x.
Second expression: If Conor buys multiple tickets, his total cost would be t * x, where t represents the number of tickets he purchases.
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 = 12.5.
Using the second expression, t * x, where x is the cost of each ticket, and t = 12.5:
Total cost = 12.5 * x
Since we don't have the actual value of x, we cannot find the exact total cost. However, we can provide an example calculation if we assume x = $10 (randomly chosen):
Total cost = 12.5 * 10
Total cost = $125
In this example, if each ticket costs $10, Conor's total cost for 12.5 tickets would be $125.
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
Let's use the second expression, t * x, to find possible values of t that would make Conor's total cost fall between $17.50 and $20.
Assuming the cost per ticket, x, is $1, we can find the possible value of t:
$17.50 < t * 1 < $20
Dividing both sides by 1:
$17.50 < t < $20
This means that any value of t between $17.50 (exclusive) and $20 (exclusive) would make Conor's total cost fall within the desired range.
For example, t = $18 or t ≈ $19.99 would both work.
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
Let's assume the cost of the set of power tools is $x.
First expression: Winona's total cost can be represented as x + d. Here, d represents any additional amount Winona decides to contribute towards the gift, in addition to the cost of the power tools.
Second expression: Takoda's total cost can be represented as x - d. Here, d represents any amount Takoda decides to deduct or contribute less towards the gift than the actual cost of the power tools.
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 result of taking a given value of d, subtracting 5 from it, and then multiplying it by 0.90 or 90%.
We know this because the expression includes the operation of subtraction (-), the value of d being subtracted by 5, and the multiplication by 0.90.
This expression could also be written as 0.90d - 4.50.
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 = $50.
For Winona, using the expression x + d where x is the cost of the power tools, and d = $50:
Total cost for Winona = x + $50
For Takoda, using the expression x - d where x is the cost of the power tools, and d = $50:
Total cost for Takoda = x - $50
Since we don't have the actual value of x, we cannot find the exact total cost. However, for this example, let's assume the cost of the power tools is x = $80.
Total cost for Winona = $80 + $50 = $130
Total cost for Takoda = $80 - $50 = $30
Based on this calculation, Winona's total cost for the gift would be $130, while Takoda's total cost would be $30. Therefore, it would be more feasible for them to choose the present where Takoda pays x - d, as it would be more affordable for him compared to Winona.
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 Pleasantville and use the second and third columns to write two expressions showing the current estimated population of the town in terms of x.
First expression: The current estimated population of Pleasantville can be represented as x - (2% of x). Here, x represents the population of Pleasantville as of the last census, and 2% of x represents the estimated decrease in population since the last census.
Second expression: The current estimated population of Pleasantville can also be represented as x - 0.02x. Simplifying this expression gives us 0.98x. This means that the current estimated population is 98% of the population as of the last census.
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 write two expressions showing the current estimated population of Concord in terms of p:
First expression: The current estimated population of Concord can be represented as p - (9% of p). Here, p represents the population of Concord as of the last census, and 9% of p represents the estimated decrease in population since the last census.
Second expression: The current estimated population of Concord can also be represented as p - 0.09p. Simplifying this expression gives us 0.91p. This means that the current estimated population is 91% of the population as of the last census.
Choose a number greater than 5,000 and less than 10,000 for the value of p.
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
Let's choose p = 6,500 as the value for the population of Concord.
Using the expression p - 0.09p to calculate the estimated current population of Concord:
Estimated current population = 6,500 - 0.09 * 6,500
Estimated current population ≈ 6,500 - 585
Estimated current population ≈ 5,915
Rounding to the nearest whole number, the estimated current population of Concord is 5,915.
I used the expression p - 0.09p because the percentage change given for Concord was -9%. To calculate the estimated current population, I subtracted 9% of the population (0.09p) from the population at the last census (p). This expression takes into account the decrease in population and provides a straightforward calculation based on the given percentage change.
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 = 1/3b .
a. Write two different expressions giving the perimeter of the donkey’s pen
To find the perimeter of the donkey's pen, we need to add up the lengths of all sides.
First expression: The perimeter of the pen can be written as P = 2a + 2b, where a is one side and b is the adjacent side. This expression accounts for each side being counted twice (since there are two equal sides of length a and two equal sides of length b) when calculating the perimeter.
Second expression: Since a = (1/3)b, we can substitute (1/3)b for a in the first expression: P = 2((1/3)b) + 2b. Simplifying this expression, we get P = (2/3)b + 2b.
Therefore, the two expressions for the perimeter of the donkey's pen are:
1) P = 2a + 2b
2) P = (2/3)b + 2b
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
Let's choose a = 10 for the value of a.
Using the second expression, P = (2/3)b + 2b, we can substitute a = 10:
P = (2/3)b + 2b
Since a = 10 and a = (1/3)b, we can substitute 10 for (1/3)b:
10 = (1/3)b
To solve for b, we multiply both sides by 3:
30 = b
Now, we can substitute the value of b back into the expression for the perimeter:
P = (2/3) * 30 + 2 * 30
P = 20 + 60
P = 80
Therefore, when a = 10, the perimeter of the donkey's pen is 80 yards.
Explain why you used that expression to evaluate the perimeter of the
donkey’s pen
I used the expression P = (2/3)b + 2b to evaluate the perimeter of the donkey's pen because it is based on the given relationship between a and b, which states that a = (1/3)b. By substituting this relationship into the expression for perimeter, we can express it solely in terms of b.
Since we were given a value for a (a = 10 in this case), substituting it into the expression allows us to solve for b. Once we find the value of b, we can substitute it back into the expression for perimeter to calculate its value.
Using this expression gives us a direct way to evaluate the perimeter based on the relationship between a and b, allowing us to find the final result.