A photo booth charges a $500 fee for two hours at a party, plus $50 per additional hour. Cindy doesn't want to spend more than $700 on the photo booth rental. What is the maximum number of additional hours (beyond the first two) that Cindy can rent the photo booth for her party?
Responses
A 3
B 4
C 5
D 6
E 7
The cost of renting the photo booth for two hours is $500. If Cindy wants to spend no more than $700, that means she has $200 left to spend on additional hours. Each additional hour costs $50. To determine the maximum number of additional hours Cindy can rent the photo booth, divide the remaining budget ($200) by the cost per additional hour ($50).
$200 / $50 = 4
Cindy can rent the photo booth for a maximum of 4 additional hours.
Therefore, the correct answer is B) 4.
Stephen and Rocco each have apps on their phones.
• The number of apps on Stephen’s phone can be represented by x.
• The number of apps on Rocco’s phone is 4 times the number of apps on Stephen’s phone.
• The total number of apps on both boys’ phones is at least 45.
What is the solution set for x, the number of apps on Stephen’s phone?
Responses
A x ≥ -9
B x ≤ 9
C x ≥ 9
D x ≤ -9
Let's set up the equation to represent the information given.
The number of apps on Stephen's phone is represented by x.
The number of apps on Rocco's phone is 4 times the number of apps on Stephen's phone, so it is 4x.
The total number of apps on both boys' phones is at least 45, so the equation is:
x + 4x ≥ 45
Combining like terms, we get:
5x ≥ 45
Dividing both sides of the inequality by 5, we get:
x ≥ 9
Therefore, the solution set for x, the number of apps on Stephen's phone, is x ≥ 9.
The correct answer is C) x ≥ 9.
George went to the store to buy notebooks.
• He had $36 to spend.
• He purchased 4 notebooks.
• After buying the notebooks, George had less than $12 left.
What is the solution set for x, the cost of each notebook?
Responses
A x > $4
B x > $3
C x > $6
D x > $5
Let's set up the equation to represent the information given.
George had $36 to spend and he purchased 4 notebooks.
The cost of each notebook can be represented by x.
The total cost of the notebooks is 4x.
After buying the notebooks, George had less than $12 left, so we can write the inequality:
36 - 4x < 12
Subtracting 36 from both sides of the inequality, we get:
-4x < 12 - 36
-4x < -24
Dividing both sides of the inequality by -4, we need to change the direction of the inequality:
x > 6
Therefore, the solution set for x, the cost of each notebook, is x > $6.
The correct answer is C) x > $6.
A catering company charges $300 plus $40 per guest for a wedding. Sarah and Eric do not want to spend more than $5,000 on catering. Write and solve an inequality in terms of the number of guests, g, that can be invited.
Responses
A 300 - 40g ≥ 5000; g ≥117
B 300 - 40g ≤ 5000; g ≤ 118
C 300 + 40g ≤ 5000; g ≤ 117
D 300 + 40g ≤ 5000; g ≤ 118
Let's set up the inequality to represent the information given.
The catering company charges $300 plus $40 per guest for a wedding.
The total cost of catering can be represented as 300 + 40g, where g is the number of guests.
Sarah and Eric do not want to spend more than $5,000 on catering.
This can be represented as 300 + 40g ≤ 5000.
To solve this inequality for the maximum number of guests that can be invited, we need to isolate g.
Subtracting 300 from both sides of the inequality, we get:
40g ≤ 5000 - 300
40g ≤ 4700
Dividing both sides of the inequality by 40, we get:
g ≤ 4700/40
g ≤ 117.5
Since the number of guests cannot be a decimal, we round down to the nearest whole number to get:
g ≤ 117
Therefore, the solution set for g, the number of guests that can be invited, is g ≤ 117.
The correct answer is A) 300 - 40g ≥ 5000; g ≥ 117.
Jasmine is on a cell phone plan where she pays $20 a month plus $0.10 per text message. She does not want to spend more than $40 on her cell phone bill. Write and solve the inequality that will tell her how many text messages she can send.
Responses
A 20 + 10x ≤ 40; She can send 2 text messages.
B 20 + 10x ≥ 40; She can send 2 text messages.
C 20 + 0.10x ≤ 40; She can send 20 text messages.
D 20 + 0.10x ≤ 40; She can send 200 text messages.
Let's set up the inequality to represent the information given.
Jasmine pays $20 a month plus $0.10 per text message.
The total cost of her cell phone bill can be represented as 20 + 0.10x, where x is the number of text messages.
Jasmine does not want to spend more than $40 on her cell phone bill.
This can be represented as 20 + 0.10x ≤ 40.
To solve this inequality for the maximum number of text messages she can send, we need to isolate x.
Subtracting 20 from both sides of the inequality, we get:
0.10x ≤ 40 - 20
0.10x ≤ 20
Dividing both sides of the inequality by 0.10, we get:
x ≤ 20/0.10
x ≤ 200
Therefore, the solution set for x, the number of text messages Jasmine can send, is x ≤ 200.
The correct answer is D) 20 + 0.10x ≤ 40; She can send 200 text messages.
The Mitchell family is renting a boat for the day. The boat rental has a flat fee of $100 plus $20 for each hour. They have to pay for a whole hour even if they are not out on the lake for a whole hour. For example, if they rent the boat for 3 and one-half hours, they have to pay for 4 hours.
If they want to spend $250 or less on the boat rental for the day, how many hours can they rent the boat? Formulate an inequality and solve.
Responses
A 100 + 20x ≤ 250; They can boat for 7 hours.
B 100 + 20x ≥ 250; They can boat for 8 hours.
C 100 + 20x ≤ 250; They can boat for 8 hours.
D 100 + 20x ≥ 250; They can boat for 7 hours.