PART A
Lauren is planning a catered dinner party for her parents' anniversary with a dinner budget of $288. She has selected two options: a chicken dinner that costs $9 per plate and a steak dinner that costs $12 per plate. Lauren is working on the guest list and must also determine how many of each meal to order.
Let x represent the number of chicken dinners and let y represent the number of steak dinners.
Complete the equation that represents this situation.
Make sure that you write the coefficient first, then the variable. For example 3 times x should be entered 3x and 5 times y should be entered 5y.
Question 2
PART B
If Lauren orders only chicken dinners, how many dinners can she order?
Enter the number in the box.
chicken dinners
Question 3
PART C
If Lauren orders only steak dinners, how many dinners can she order?
Enter the number in the box.
PART A:
The equation that represents this situation is:
9x + 12y = 288
PART B:
If Lauren orders only chicken dinners, the equation becomes:
9x = 288
To solve for x, divide both sides by 9:
x = 32
Therefore, Lauren can order 32 chicken dinners.
PART C:
If Lauren orders only steak dinners, the equation becomes:
12y = 288
To solve for y, divide both sides by 12:
y = 24
Therefore, Lauren can order 24 steak dinners.
Roman has $40 to spend on snacks for his camping trip. He plans to buy protein bars that cost $3 each and individual bags of trail mix that cost $2 each.
If x represents the number of protein bars that Roman buys and y represents the number of individual bags of trail mix that Roman buys, then which equations represent this situation?
Choose 2.
The two equations that represent this situation are:
3x + 2y = 40 (equation representing the total cost of the protein bars and bags of trail mix)
x + y = 20 (equation representing the total number of snacks Roman buys)
An office machine purchased new for $3600 loses $400 each year.
Question 1
Assume the value continues to decrease the same amount each year. If f(x) represents the value of the office machine after x years, which linear function models the given situation?
Responses
A f(x) = 400x + 3600f(x) = 400x + 3600
B f(x) = −400x − 3600f(x) = −400x − 3600
C f(x) = −400x + 3600f(x) = −400x + 3600
D f(x) = 400x − 3600f(x) = 400x − 3600
Question 2
How many years will it take for the office machine's value to equal zero?
Responses
A 55
B 66
C 99
D 12
Question 1:
The correct linear function that models the given situation is:
C) f(x) = -400x + 3600
Question 2:
To find the number of years it will take for the office machine's value to equal zero, we can set f(x) equal to zero and solve for x:
-400x + 3600 = 0
Subtract 3600 from both sides:
-400x = -3600
Divide both sides by -400:
x = 9
Therefore, it will take 9 years for the office machine's value to equal zero.
Martha is printing brochures for Barton Middle School’s STEM Night. The printing company charges a printing fee plus an additional fee per brochure printed. The table shows the linear relationship between the number of brochures and the total cost of printing, including the printing fee.
Printing
Number of Brochures, x Total Cost, y
40 $600.00
43 $607.50
45 $612.50
52 $630.00
55 $637.50
Which statement is true?
Responses
A The additional fee per brochure is $7.50.The additional fee per brochure is $7.50.
B The printing fee is $2.50.The printing fee is $2.50.
C The additional fee per brochure is $2.50.The additional fee per brochure is $2.50.
D The printing fee is $250.
To determine the additional fee per brochure, we need to find the difference in cost when the number of brochures increases by 1.
From the data given:
- When the number of brochures goes from 40 to 43, the total cost increases by $607.50 - $600.00 = $7.50.
- When the number of brochures goes from 43 to 45, the total cost increases by $612.50 - $607.50 = $5.00.
- When the number of brochures goes from 45 to 52, the total cost increases by $630.00 - $612.50 = $17.50.
- When the number of brochures goes from 52 to 55, the total cost increases by $637.50 - $630.00 = $7.50.
The additional fee per brochure remains constant at $7.50 for all increases in the number of brochures.
Therefore, the statement that is true is:
A) The additional fee per brochure is $7.50.
The temperature of a substance was recorded over several minutes, as shown in the graph below. The graph displays the linear relationship between the temperature (measured in degrees Celsius) and the number of minutes the substance was being observed.
Temperature Over Time
Temperature (°C)
Time (Minutes)
Which statement best describes the slope of the graph?
Responses
A The temperature is increasing 3.25°C each minute.The temperature is increasing 3.25°C each minute.
B The temperature is increasing 5.25°C each minute.The temperature is increasing 5.25°C each minute.
C The temperature is increasing 1.25°C each minute.The temperature is increasing 1.25°C each minute.
D The temperature is increasing 7.25° C each minute.
To determine the slope of the graph, we need to look at the change in temperature (ΔT) divided by the change in time (Δt).
Looking at the graph, we can see that for every 1 unit increase in time (minute), the temperature increases by approximately 4 units (degrees Celsius).
Therefore, the statement that best describes the slope of the graph is:
A) The temperature is increasing 4°C each minute.