1.a Interpreting Linear Functions
Sandra makes necklaces and sells them at a school craft fair. She used the equation
P = 7.5n - (2.25n + 15)
Based on this equation, how much does she charge for each necklace?
$7.50 per necklace.
An equation is shown.
3x - 7 = 2(x + 3)
Solve for X
X = 13
The school is planning to order custom t-shirts for the 8th grade class. The cost of the design is $150 and each shirt will cost $35 to produce. The school budgeted $4000 to purchase shirts.
Write an equation and use it to solve for the number of t-shirts the school can purchase.
4000=35x+150
x=110
The steps to correctly solve an equation are shown below. Complete the table.
Step Equation Reason
1 4(x + 7)=9x - 7 Given
2 4x + 28 = 9x - 7 ?
3 28 = 5x - 7 ?
4 35 = 5x ?
5 7 = x ?
Step 1 Given , Step 2 Distributive property , Step 3 Combine like terms , Step 4 Add 7 to both sides , Step 5 Divide both sides by 5.
Tyler has at most $10 to spend at the store. Tyler plans on purchasing a soda for $1.50, a candy bar for $0.75 and bananas that cost $1.15 per pound.
Write an inequality that represents Tyler’s planned purchase.
Solve the inequality for the possible number of pounds of bananas that Tyler can purchase.
1.50+0.75+1.15x ≤ 10
x ≤ 6.74
A car leaves Athens, GA, and travels west towards Atlanta, GA. The equation is D = 72 - 59t
In this equation what does the 59 represent ?
Speed of the car / Miles per hour
Determine the number of solutions in the equation below:
4x - 6 = 2(2x - 3)
Infinitely many solutions
The perimeter of a rectangular deck is 32 feet.
L = 3x + 6
W = 2x
Find the dimensions of the deck in terms of feet. What is the Perimeter?
The deck is 12 feet by 4 feet.
P = 32 ft
The steps to correctly solve an equation are shown below. Complete the table.
Step Equation Reason
1 -3(x-6)=6 Given
2 Distributive property
3 Subtract
4 Divide
5 Answer
Step 1 -3(x-6)=6
Step 2 -3x +18 = 6
Step 3 -3x = -12
Step 4 x = -12/-3
Step 5 x = 4
The 8th grade class needs to purchase a park permit for $250.00 for their upcoming class picnic. Each eighth grader attending the picnic pays $0.75. Each guest pays $1.25.
If 200 8th grade students attend the picnic, which inequality can be used to determine the number of guests, x, needed to cost the cover of the permit?
A. 0.75x + 1.25(200) < 250; 80 guests
B. 0.75x + 1.25(200) > 250; 80 guests
C. 0.75(200) + 1.25x > 250; 80 guests
D. 0.75(200) + 1.25x < 250; 80 guests
C . 0.75(200) + 1.25x > 250
The cost of running an ad on youtube is modeled by the function: C(n)= 110n + 900. Where n is the number of times the ad plays.
How much does the ad cost? How much does each ad play cost?
ad cost = 900
each ad play cost = 110
Determine the number of solutions in the equation below:
2x + 3 = 2(x + 2.5)
No Solution
Alex is selling tickets to the school play. A student ticket costs $4.00 and an adult ticket costs $6.50. Alex sells x adult tickets and 12 student tickets.
Write a equation that represents how much money Alex collected from selling tickets.
Total=6.5x+48
When solving the equation
4(3x + 2) - 9 = 8x + 7
For her first step, Emily wrote:
4(3x + 2) = 8x + 16
What property justifies Emily’s first step?
Addition Property of Equality
Whatever you do to one side, you must do to the other.
Jason’s part time job pays him $155 each week. If he already has $75 saved, what is the minimum number of weeks he needs to work in order to have enough money to buy a Playstation 5 for $500?
x ≥ 2.74
3 weeks (round up)
A plumber has a set fee for a house call and charges by the hour for repairs. The total cost of her services can be modeled by: c(t) = 125t + 95
Which statements about the function are true?
I A house call fee costs $95
II The plumber charges $125 per hour
III The number of hours the job takes is represented by t
Statements 1 , 2 , & 3 are TRUE
Determine the number of solutions in the equation below:
17 + 5(2x - 9) = 4 - 2x + 7
One Solution
A marine biology class at the high school is researching the cost of visiting the Georgia Aquarium for a private tour. Georgia aquarium tickets cost $53 per ticket and $245 for the private tour guide.
Write an equation to represent the total cost of visiting the aquarium.
How much will it cost for 55 people to attend?
C(x)=53x +245
Cost for 55 people: $3,160
When solving for x in the equation 4(x - 1) + 3 = 18, Aaron completed the table below.
Step Equation
1 4(x - 1) + 3 = 18
2 4(x - 1) = 15
3 4x - 1 = 15
4 4x = 16
5 x = 4
Which property was incorrectly used when going from step 2 to step 3?
Distributive Property
An ice cream shop sells ice cream cones, c, and milkshakes m. Each ice cream cone costs $1.50 and each milkshake costs $2.00.
De’Mann has $19.00 to spend on ice cream cones and milkshakes. If he must buy 5 ice cream cones, which inequality could be used to determine the maximum number of milkshakes he can buy?
A. 1.50(5) + 2.00m > 19.00
B. 1.50(5) + 2.00m < 19.00
C. 1.50c + 2.00(5) > 19.00
D. 1.50c + 2.00(5) < 19.00
B. 1.50(5) + 2.00m < 19.00