Jason got a new mp3 player for his birthday. He is very excited to get started downloading songs. He looks online and finds two companies that offer different pricing options for song downloads. Company A charges $1.25 per song. Company B charges $0.65 per song plus a one-time $4 membership fee.
What is the maximum number of songs that can be purchased in order for Company A to be a better buy?
We need to compare the total cost of purchasing x number of songs from each company.
For Company A:
Total cost = $1.25 x (number of songs)
For Company B:
Total cost = $0.65 x (number of songs) + $4
We want to find the maximum number of songs where Company A is the better buy. This means we want to find the point where the total cost of Company A is less than or equal to the total cost of Company B.
$1.25 x = $0.65 x + $4
Simplifying and solving for x:
$0.60 x = $4
x = 6.67
Since you can't buy a fractional number of songs, we should round down to the nearest whole number.
Therefore, the maximum number of songs that can be purchased in order for Company A to be a better buy is 6.
Joseph is going on a trip and he needs to rent a car. He looks online and finds two companies that offer different pricing options for car rentals. Company A charges $0.25 per mile plus a $50 rental fee. Company B charges $0.45 per mile plus a $20 rental fee.
What is the minimum number of miles that Joseph must drive in order for Company A to be a better buy? The company charges only for whole number mileage (not fractional increments of miles driven).
Responses
A 149 miles149 miles
B 150 miles150 miles
C 151 miles151 miles
D 175 miles175 miles
E 125 miles
We need to compare the total cost of renting a car from each company based on the number of miles Joseph drives.
For Company A:
Total cost = $0.25 x (number of miles) + $50
For Company B:
Total cost = $0.45 x (number of miles) + $20
We want to find the minimum number of miles where Company A is the better buy. This means we want to find the point where the total cost of Company A is less than or equal to the total cost of Company B.
$0.25 x + $50 = $0.45 x + $20
Simplifying and solving for x:
$0.20 x = $30
x = 150
Therefore, the minimum number of miles that Joseph must drive in order for Company A to be a better buy is 150 miles.
Becky graphs a system of two linear equations and determines that (1,5) and (3,7) are solutions. What does the graph of the system look like? How many solutions are possible?
Responses
A one line; infinitely manyone line; infinitely many
B two lines; one solutiontwo lines; one solution
C two lines; two solutionstwo lines; two solutions
D curve; two solutions
B. The graph of the system would consist of two lines since there are two linear equations and two given solutions. Since the lines intersect at exactly one point, there is only one solution for the system.
Sara is serving wings and burgers at her party. Wings cost $6.00 per serving and burgers are $3.00 each. Sara knows that at least 4 of her friends want wings. Sara must spend less than $45.00. Sara graphs a system of inequalities to determine how many servings of each kind of food she could serve to stay within her budget.
According to the dark blue area on the graph, what is the maximum number of burgers that Sara could serve with 6 servings of wings?
Responses
A 3
B 5
C 4
D 2
B. According to the dark blue area on the graph, the maximum number of burgers that Sara could serve with 6 servings of wings is 5.
The sum of x and y is greater than 0. When y is subtracted from x, the difference is less than or equal to 0. Which system of inequalities could you use to solve for x and y?
Responses
A x + y > 0 and x − y
B x + y > 0 and x − y
C x − y > 0 and x + y
D x + y < 0 and x − y
B.
The given information can be translated into two inequalities:
x + y > 0 (the sum of x and y is greater than 0)
x - y ≤ 0 (when y is subtracted from x, the difference is less than or equal to 0)
Therefore, the system of inequalities to solve for x and y would be:
x + y > 0
x - y ≤ 0
If two equations are graphed, how can you find the solution to the system of equations?
Responses
A Find where the lines intersect.Find where the lines intersect.
B Find where the slope is positive.Find where the slope is positive.
C Find the slope of point lines.Find the slope of point lines.
D Find where both lines cross the y-axis.Find where both lines cross the y-axis.
E Find where both lines cross the x-axis.