The 1. 2. and 3. are there so you can write that down, so I know what you're talking about.
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.
1.Conor buys a ticket to see a movie. Write two expressions in terms of t
showing his total cost.
2.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.
3. 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?
1. The first expression in terms of t showing Conor's total cost would be: t + (0.15*t).
2. Let's assume t = $12.50.
Using the first expression from part a, his total cost would be: $12.50 + (0.15*$12.50) = $12.50 + $1.875 = $14.375.
Rounded to the nearest penny, Conor's total cost would be approximately $14.38.
3. To find a possible value of t that makes Conor's total cost between $17.50 and $20, we can set up an equation:
17.50 < t + (0.15*t) < 20.
By trial and error, we can find that t = $15 satisfies this inequality.
The 1. 2. and 3. are there so you can write that down, so I know what you're talking about.
Winona and Takoda are shopping for a present for their mother. They find a set of
power tools with a price tag of $d.
In the following table, the column titled Cost shows the cost of the power tools.
compared with the costs of the two other presents: water skis and jewelry.
All three items are on sale. The column titled Discount shows the percentage discount
for each item.
There is no sales tax in the state where they live.
Present Cost ($) Discount (%) Total Paid
Power tools d 15%
Water skis d + 15 25%
Jewelry d – 5 10%
1. 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.
2. What does the expression 0.90(d – 5) refer to? How do you know? How else
could this expression be written?
3.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.
1. The first expression 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 is: d + (0.15*d).
2. The expression 0.90(d - 5) refers to the total cost of the jewelry after a 10% discount has been applied. We know this because 0.90 represents 90% of the original cost and (d - 5) represents the original cost of the jewelry after a 5% discount has been applied. This expression could also be written as: 0.90d - 4.5.
3. Let's choose a value of d = $50.
The total cost of the power tools would be: $50 + (0.15*$50) = $50 + $7.50 = $57.50.
The total cost of the water skis would be: $50 + 15 = $65.
The total cost of the jewelry would be: $50 - 5 = $45.
Based on the prices, Winona and Takoda should buy the jewelry for their mother. It is the least expensive option at $45, making it the most cost-effective choice. Furthermore, it is on sale with a 10% discount, which adds to the affordability.
The 1. 2. and 3. are there so you can write that down, so I know what you're talking about.
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%
1.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.
2. 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.
3. 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
1. Let's choose the town of Pleasantville.
The first expression for the current estimated population of Pleasantville in terms of x would be: x - (0.02*x).
The second expression for the current estimated population of Pleasantville in terms of x would be: x * (1 - 0.02).
2. Adding a fourth row for the town of Concord:
Town | Census Population | Percentage Change
Concord | p | -9%
The first expression for the current estimated population of Concord in terms of p would be: p + (-0.09*p).
The second expression for the current estimated population of Concord in terms of p would be: p * (1 - 0.09).
3. Let's choose p = 8,000.
Using the second expression for Concord's estimated population, the calculation would be: 8,000 * (1 - 0.09) = 8,000 * 0.91 = 7,280.
Rounding to the nearest whole number, the estimated current population of Concord would be 7,280.
I used the second expression (p * (1 - 0.09)) to calculate the estimated current population of Concord because it takes into account the percentage decrease of -9% and applies it to the census population of p. This allows us to calculate a new population estimate by subtracting 9% from the original population.
Help me rq you did not explain this.
Town Census Population Percentage change
PL x -2%
AC y +5%
HC z +7%
1. Let's choose the town of Pleasantville (PL).
The second column states that the census population of Pleasantville is x.
The third column states that there is a percentage change of -2% in the population.
To calculate the current estimated population of Pleasantville in terms of x, we can use the following expressions:
First expression: x - (0.02 * x)
Explanation: We take the census population x and subtract 2% of x to account for the decrease.
Second expression: x * (1 - 0.02)
Explanation: We multiply the census population x by the decimal equivalent of (1 - 0.02), which represents 98% of x, to calculate the current estimated population.
2. Adding a fourth row for the town of Concord (CO):
Town | Census Population | Percentage Change
Concord | p | -9%
The second column states that the census population of Concord is p.
The third column states that there is a percentage change of -9% in the population.
To calculate the current estimated population of Concord in terms of p, we can use the following expressions:
First expression: p + (-0.09 * p)
Explanation: We take the census population p and add the product of -9% of p to account for the decrease.
Second expression: p * (1 - 0.09)
Explanation: We multiply the census population p by the decimal equivalent of (1 - 0.09), which represents 91% of p, to calculate the current estimated population.
3. Let's choose p = 8,000.
Using the second expression, the calculation would be: 8,000 * (1 - 0.09) = 8,000 * 0.91 = 7,280.
I used the second expression (p * (1 - 0.09)) to calculate the estimated current population of Concord because it takes into account the percentage decrease of -9% and applies it to the census population of p. This allows us to calculate a new population estimate by subtracting 9% from the original population.
The 1. 2. and 3. are there so you can write that down, so I know what you're talking about.
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
.
1. Write two different expressions giving the perimeter of the donkey’s pen.
2. 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.
3. Explain why you used that expression to evaluate the perimeter of the
donkey’s pen
1. The perimeter of the donkey's pen can be calculated using the following two expressions:
Expression 1: 2a + 2b
Explanation: This expression adds up the lengths of all four sides of the rectangle (two sides measuring a yards and two sides measuring b yards) to find the perimeter.
Expression 2: 2(a + b)
Explanation: This expression simplifies the addition in Expression 1 by combining the two lengths a and b first, and then multiplying the sum by 2 to find the perimeter.
2. Let's choose a = 9.
Using Expression 1 to evaluate the perimeter, we get: 2(9) + 2b = 18 + 2b
Since we don't know the value of b, we cannot calculate the exact perimeter of the pen without more information.
3. I used Expression 1 (2a + 2b) to evaluate the perimeter of the donkey's pen because it considers the lengths of each side individually (a and b) and adds them up to find the total length around the pen. This accounts for the fact that the sides can have different lengths. However, without knowing the value of b, we cannot calculate the exact perimeter.
The 1. 2. and 3. are there so you can write that down, so I know what you're talking about.
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.
.
1. Write two different expressions giving the perimeter of the donkey’s pen.
2. 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.
3. Explain why you used that expression to evaluate the perimeter of the
donkey’s pen
1. The perimeter of the donkey's pen can be calculated using the following two expressions:
Expression 1: 2a + 2b
Explanation: This expression adds up the lengths of all four sides of the rectangle (two sides measuring a yards and two sides measuring b yards) to find the perimeter.
Expression 2: 2(a + b)
Explanation: This expression simplifies the addition in Expression 1 by combining the two lengths, a and b, first and then multiplying the sum by 2 to find the perimeter.
2. Let's choose a = 9.
Since a = (1/3)b, we can substitute 9 for a in the equation to find the value of b:
9 = (1/3)b
Multiplying both sides of the equation by 3 yields:
27 = b
Now we have a = 9 and b = 27.
Using Expression 2 to evaluate the perimeter, we get: 2(9 + 27) = 2(36) = 72 yards.
Thus, the perimeter of the pen is 72 yards.
3. I used Expression 2 (2(a + b)) to evaluate the perimeter of the donkey's pen because it simplifies the addition of a and b into a single expression, making the calculation more concise. Additionally, Expression 2 allows for the use of the given relationship between a and b, which is that a equals one-third of b. By using this expression, we can easily substitute the given value of a and solve for b to find both sides of the rectangle and ultimately calculate the perimeter.
The 1. 2. are there so you can write that down, so I know what you're talking about.
Farah plans to buy a vintage toy online for $x. The cost includes a shipping fee of $y
and a handling fee of 9% of $x.
1. Write two expressions showing the total amount of money Farah should expect
to pay.
2. Before Farah can make the purchase, she gets good news: the shipping fee has
been waived, and the toy she wants to buy has been put on sale for a discount
of between 2% and 8%. Choose the value of the discount. Then write two
expressions showing the amount of money Farah should expect to pay now
1. The two expressions showing the total amount of money Farah should expect to pay are:
Expression 1: x + y + 0.09x
Explanation: This expression adds the cost of the toy x, the shipping fee y, and the handling fee 9% of x to calculate the total amount of money Farah should expect to pay.
Expression 2: 1.09x + y
Explanation: This expression combines the cost of the toy x after adding the handling fee (1.09x) and the shipping fee y to calculate the total amount of money Farah should expect to pay.
2. Let's choose a discount of 5%.
After the shipping fee has been waived and the toy is on sale with a 5% discount, the expressions showing the amount of money Farah should expect to pay now are:
Expression 1: (0.95 * x) + 0
Explanation: This expression subtracts the discount of 5% from the cost of the toy x, and since the shipping fee is waived, there is no additional cost to consider.
Expression 2: 0.95x
Explanation: This expression simplifies Expression 1 by only considering the discounted cost of the toy (0.95x) now that the shipping fee is waived.
In both expressions, we only consider the cost of the toy after applying the discount and exclude any additional fees since the shipping fee has been waived.
The 1. 2. and 3. are there so you can write that down, so I know what you're talking about.
A tool manufacturer produces a special toolbox consisting of two kinds of tools:
wrenches and screwdrivers. There are t tools in all in each box. The number of
wrenches is given by the variable w and the number of screwdrivers is given by the
variable s.
1. What does the expression t – s stand for in this scenario? How does that relate
to the expression t – w? How else could you write an expression to show this
relationship?
2. The tool company decides to decrease the number of screwdrivers in each box
by 5 while increasing the number of wrenches by 50%. Write two expressions
to show these changes, using the variables s and w.
3. Use one of the expressions you wrote in part b. Find values for w and s that
would result in an increase in the total number of tools in the new box. Then
find values that would result in a decrease in the total number of tools in the
new box. Explain why you chose the expression that you did
1. In this scenario, the expression t - s represents the number of wrenches in the toolbox. This is because t is the total number of tools in the box, and when we subtract the number of screwdrivers (s) from the total, we are left with the number of wrenches (w).
The expression t - w represents the number of screwdrivers in the toolbox. This is because when we subtract the number of wrenches (w) from the total number of tools (t), we are left with the number of screwdrivers (s).
We can write an expression to show this relationship by using the expression t - s and exchanging the variables:
w = t - s
2. If the tool company decreases the number of screwdrivers by 5 and increases the number of wrenches by 50%, we can write the following expressions:
Expression 1: w + 0.5w
Explanation: This expression represents an increase of 50% in the number of wrenches (w). Adding 0.5w to the original number of wrenches gives us the new number of wrenches.
Expression 2: s - 5
Explanation: This expression represents a decrease of 5 in the number of screwdrivers (s). Subtracting 5 from the original number of screwdrivers gives us the new number of screwdrivers.
3. Let's use Expression 1 from part 2 (w + 0.5w) to find values for w and s that would result in an increase or decrease in the total number of tools in the new box.
To result in an increase in the total number of tools, we need w + 0.5w to be greater than t. Let's choose t = 10 tools. We can try different values for w and s to see if the total number of tools increases.
If w = 5 and s = 3:
w + 0.5w = 5 + 0.5(5) = 5 + 2.5 = 7.5
The total number of tools is 7.5 + 3 = 10.5, which is greater than the original 10 tools. Therefore, the total number of tools in the new box would increase.
To result in a decrease in the total number of tools, we need w + 0.5w to be less than t. Let's choose t = 15 tools and try different