The cooking club sells stickers featuring Featherbrain the Turkey, the school's mascot. In one hour, they sell $fifty five worth of stickers. Each member who sells stickers is paid $two. Represent earnings from selling stickers as positive and costs of paying members as negative.
Define a unit for the amount of money the club will make.
How much money will the club make if nine members sell stickers?
How much money will the club make if six members sell stickers?
Complete the rows for the amount paid to each member and the income from selling stickers. Then, enter a variable for the number of members who sell stickers and use this variable to write an expression for the amount of money the club will make.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Members
Money Made
Unit
members
How much money will the club make if nine members sell stickers?
Question 1
How much money will the club make if six members sell stickers?
Question 2
Cost of paying each member
dollars per member
Earnings from selling stickers
dollars
Expression
Quantity Name | Members | Money Made
--------------------------------------------
Unit | members | $
--------------------------------------------
How much money will the club make if nine members sell stickers? | 9 | $
--------------------------------------------------------------
How much money will the club make if six members sell stickers? | 6 | $
--------------------------------------------------------------
Cost of paying each member | | -$2/member
--------------------------------------------------------------
Earnings from selling stickers | | +$55
--------------------------------------------------------------
Expression | x | $55 - $2x
How much money will the club make if nine members sell stickers?
How much money will the club make if six members sell stickers?
To find out how much money the club will make if nine members sell stickers, we can substitute 9 for x in the expression:
Money made = $55 - $2x
Money made = $55 - $2(9)
Money made = $55 - $18
Money made = $37
Therefore, the club will make $37 if nine members sell stickers.
To find out how much money the club will make if six members sell stickers, we can substitute 6 for x in the expression:
Money made = $55 - $2x
Money made = $55 - $2(6)
Money made = $55 - $12
Money made = $43
Therefore, the club will make $43 if six members sell stickers.
After her alarm rings, Daisy has fifty-five minutes to get ready. She stays in bed one minute after the alarm rings the first day. She stays in bed for two minutes after the alarm rings the second day. She stays in bed three minutes after the alarm rings the third day, and so on.
Define units for the number of days and the time Daisy has to get ready.
How much time will she have to get ready after the alarm rings on the 29th day?
When Daisy is down to sixteen minutes to get ready, how many days has it been?
Complete the rows for the number of additional minutes that Daisy snoozes each day and the time Daisy has to get ready when her alarm rings. Then, enter a variable for the number of days and use this variable to write an expression for the time Daisy has to get ready.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Number of Days
Time to Get Ready
Unit
How much time will she have to get ready after the alarm rings on the 29th day?
Question 1
When Daisy is down to sixteen minutes to get ready, how many days has it been?
Question 2
Change in time to get ready each day
minutes per day
Time to get ready when alarm rings
minutes
Expression
Quantity Name | Number of Days | Time to Get Ready
-----------------------------------------------------------------
Unit | days | min
-----------------------------------------------------------------
How much time will she have to get ready after the alarm rings on the 29th day? | 29 | $
---------------------------------------------------------------------------------------
When Daisy is down to sixteen minutes to get ready, how many days has it been? | | 16
---------------------------------------------------------------------------------------
Change in time to get ready each day | | +1 minute/day
---------------------------------------------------------------------------------------
Time to get ready when alarm rings | x | $
---------------------------------------------------------------------------------------
Expression | x | 55 - (1+2+3+...+(x-1))
Note: The formula for the sum of the first n positive integers is n(n+1)/2. Therefore, the sum of the first (x-1) positive integers is (x-1)(x-1+1)/2, which simplifies to (x-1)x/2 or (x^2-x)/2.
So, the expression for the time Daisy has to get ready when the alarm rings is:
Time to get ready when alarm rings = 55 - (1 + 2 + 3 + ... + (x-1))
Time to get ready when alarm rings = 55 - [(x^2 - x)/2]
Time to get ready when alarm rings = 55 - (x^2 - x)/2
Time to get ready when alarm rings = (2(55) - x^2 + x)/2
To find out how much time Daisy will have to get ready on the 29th day, we can substitute 29 for x in the expression:
Time to get ready = (2(55) - x^2 + x)/2
Time to get ready = (2(55) - 29^2 + 29)/2
Time to get ready = (110 - 841 + 29)/2
Time to get ready = -351/2 (since the answer is negative, Daisy will not have any time to get ready)
To find out how many days it has been when Daisy is down to sixteen minutes to get ready, we can substitute 16 for the time to get ready in the expression:
16 = (2(55) - x^2 + x)/2
32 = 110 - x^2 + x
x^2 - x - 78 = 0
(x - 9)(x + 8) = 0
Since the number of days cannot be negative, we have:
x = 9
Therefore, when Daisy is down to sixteen minutes to get ready, it has been nine days.
How much time will she have to get ready after the alarm rings on the 29th day?
When Daisy is down to sixteen minutes
I apologize for the previous response, as an AI language model I made a mistake in understanding the problem. Here's the correct solution:
To find out how much time Daisy will have to get ready on the 29th day, we need to find out how many minutes she will stay in bed on the 29th day and subtract that from the total time she has to get ready.
From the problem statement, we know that Daisy stays in bed for one more minute each day than the previous day. So, on the 29th day, she will stay in bed for 29 minutes.
The total time Daisy has to get ready is 55 minutes minus the total number of minutes she stays in bed. To find the total number of minutes she stays in bed over 29 days, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(a1 + an)
where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.
In this case, the first term is 1 (the number of minutes she stays in bed on the first day) and the common difference is 1 (she stays in bed for one more minute each day). So, the nth term is (n-1) + 1 = n.
Substituting these values into the formula, we get:
Sn = (n/2)(a1 + an)
Sn = (29/2)(1 + 29)
Sn = 435
So, over 29 days, Daisy stays in bed for a total of 435 minutes. Therefore, her total time to get ready on the 29th day is:
Time to get ready = 55 - 435
Time to get ready = -380
Since the answer is negative, Daisy will not have any time to get ready on the 29th day.
To answer the second question, when Daisy is down to sixteen minutes to get ready, we can use the same formula and solve for the number of days:
Time to get ready = 55 - (1 + 2 + 3 + ... + (n-1))
16 = 55 - (n-1)n/2
n^2 - n - 78 = 0
(n - 8)(n + 9) = 0
Since the number of days cannot be negative, the answer is:
n = 8
Therefore, when Daisy has sixteen minutes to get ready, it has been eight days.
How much time will she have to get ready after the alarm rings on the 29th day?
When Daisy is down to sixteen minutes to get ready, how many days has it been?
To find out how much time Daisy will have to get ready on the 29th day, we need to find out how many minutes she will stay in bed on the 29th day and subtract that from the total time she has to get ready.
From the problem statement, we know that Daisy stays in bed for one more minute each day than the previous day. So, on the 29th day, she will stay in bed for 29 minutes.
The total time Daisy has to get ready is 55 minutes minus the total number of minutes she stays in bed. To find the total number of minutes she stays in bed over 29 days, we can use the formula for the sum of an arithmetic series:
Sn = (n/2)(a1 + an)
where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term.
In this case, the first term is 1 (the number of minutes she stays in bed on the first day) and the common difference is 1 (she stays in bed for one more minute each day). So, the nth term is (n-1) + 1 = n.
Substituting these values into the formula, we get:
Sn = (n/2)(a1 + an)
Sn = (29/2)(1 + 29)
Sn = 435
So, over 29 days, Daisy stays in bed for a total of 435 minutes. Therefore, her total time to get ready on the 29th day is:
Time to get ready = 55 - 435
Time to get ready = -380
Since the answer is negative, Daisy will not have any time to get ready on the 29th day.
To find out how many days it has been when Daisy is down to sixteen minutes to get ready, we can use the same formula and solve for the number of days:
Time to get ready = 55 - (1 + 2 + 3 + ... + (n-1))
16 = 55 - (n-1)n/2
n^2 - n - 78 = 0
(n - 8)(n + 9) = 0
Since the number of days cannot be negative, the answer is:
n = 8
Therefore, when Daisy has sixteen minutes to get ready, it has been eight days.
How many minutes did it take before the student council was able to pay off their debt?
The problem statement does not provide enough information to determine how long it took to pay off the debt. Please provide more details or context about the student council's debt and any given information related to it.
After ten minutes of mud fight ticket sales, what was the balance?
How many minutes did it take before the student council was able to pay off their debt?
What was the balance in the student council fund after the first twelve minutes of ticket sales?
I apologize for my previous response. Since there was not any information about the student council. I assumed that there was no context to answer the question.
Now moving on to the new question regarding mud fight ticket sales, to answer the given questions, we need additional information such as the rate of ticket sales, the initial balance of the account, and the amount of debt.
Without that information, we cannot determine the answers to these questions. Please provide more details or context about the mud fight ticket sales problem to proceed.
The student council starts the year with a balance of $negative thirty (they were in debt). It comes up with the idea to sell tickets to a student versus teachers mud fight. The student council fund is now growing by $ten a minute.
Define units for the time selling tickets and the balance in the account.
After ten minutes of mud fight ticket sales, what was the balance?
How many minutes did it take before the student council was able to pay off their debt?
What was the balance in the student council fund after the first twelve minutes of ticket sales?
Complete the rows for the rate at which the fund grew and the balance at the start of the year. Then, enter a variable for the time selling tickets and use this variable to write an expression for the balance in the account.
Quantity Name | Time Selling Tickets | Balance in Account
--------------------------------------------------------
Unit | minutes | $
--------------------------------------------------------
After ten minutes of mud fight ticket sales, what was the balance? | 10 | $-200
--------------------------------------------------------
How many minutes did it take before the student council was able to pay off their debt? | |
--------------------------------------------------------
What was the balance in the student council fund after the first twelve minutes of ticket sales? | 12 |
--------------------------------------------------------
Rate of Fund Growth | Balance at Start of Year
----------------------------------------------
$10/minute | -$30
----------------------------------------------
Expression:
Balance in Account = $10*(Time Selling Tickets) + (-$30)
To find out how many minutes it took before the student council was able to pay off their debt, we first need to determine how much the debt is. From the problem statement, we know that the student council starts the year with a balance of -$30, so that is the amount of their debt.
When the balance in the account is positive, then the student council has paid off their debt. Using the expression above, we can solve for Time Selling Tickets:
$10*(Time Selling Tickets) + (-$30) = $0
$10*(Time Selling Tickets) = $30
Time Selling Tickets = 3 minutes
Therefore, it took 3 minutes of mud fight ticket sales for the student council to pay off their debt.
To find out the balance in the student council fund after the first twelve minutes of ticket sales, we can substitute 12 for Time Selling Tickets in the expression:
Balance in Account = $10*(Time Selling Tickets) + (-$30)
Balance in Account = $10*(12) + (-$30)
Balance in Account = $120 - $30
Balance in Account = $90
Therefore, the balance in the student council fund after the first twelve minutes of ticket sales is $90.
The student council starts the year with a balance of $negative thirty (they were in debt). It comes up with the idea to sell tickets to a student versus teachers mud fight. The student council fund is now growing by $ten a minute.
Define units for the time selling tickets and the balance in the account.
After ten minutes of mud fight ticket sales, what was the balance?
How many minutes did it take before the student council was able to pay off their debt?
What was the balance in the student council fund after the first twelve minutes of ticket sales?
Complete the rows for the rate at which the fund grew and the balance at the start of the year. Then, enter a variable for the time selling tickets and use this variable to write an expression for the balance in the account.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Time Selling Tickets
Balance in Account
Unit
After ten minutes of mud fight ticket sales, what was the balance?
Question 1
How many minutes did it take before the student council was able to pay off their debt?
Question 2
What was the balance in the student council fund after the first twelve minutes of ticket sales?
Question 3
Change in fund balance each minute
dollars per minute
Initial balance in fund
dollars
Expression
Quantity Name | Time Selling Tickets | Balance in Account
--------------------------------------------------------------------
Unit | minutes | $
--------------------------------------------------------------------
After ten minutes of mud fight ticket sales, what was the balance? | 10 | $-200
--------------------------------------------------------------------
How many minutes did it take before the student council was able to pay off their debt? | | 3
--------------------------------------------------------------------
What was the balance in the student council fund after the first twelve minutes of ticket sales? | 12 | $90
--------------------------------------------------------------------
Change in fund balance each minute | | $10/min
--------------------------------------------------------------------
Initial balance in fund | | -$30
--------------------------------------------------------------------
Expression | x | $10*x - $30
Ms. Deutsch needs four parent volunteers to help students get on and off stage at the dance recital. He also needs four parent volunteers per room of students.
Ms. Deutsch determines she will need five rooms for students at the recital. How many parent volunteers will Ms. Deutsch need in all?
On the day of the recital, Ms. Deutsch uses twelve parent volunteers. How many backstage rooms were there?
Complete the rows for the number of parent volunteers per room and the number of parent volunteers needed to help students get on and off stage. Then, enter a variable for the number of rooms of students and use this variable to write an expression for the number of parent volunteers needed.
Use the Worksheet to complete the problem. The column labels describe the quantity from the problem scenario that the column is about. The row labels describe the type of value that goes in the row: quantity descriptions, units of measure, algebraic expressions, or numeric values to answer a question.
Quantity Name
Rooms
Parent Volunteers
Unit
rooms
parent volunteers
Ms. Deutsch determines she will need five rooms for students at the recital. How many parent volunteers will Ms. Deutsch need in all?
Question 1
On the day of the recital, Ms. Deutsch uses twelve parent volunteers. How many backstage rooms were there?
Question 2
Volunteers per room
parent volunteers per room
Volunteers helping on stage
parent volunteers
Expression