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WorksheetsAlgebraic Reasoning - Solving Linear & Quadratic Word Problems
Total questions: 48
Worksheet time: 4hrs 0mins
T-shirts were on sale for $15 each and hoodies were on sale for $20 each. If she spent $150 total, write an equation to represent this situation.
Sam ordered 4 tacos and 5 enchiladas for lunch at the restaurant. His bill came to $10.80. Which equation matches the given situation?
4x + 3y = 8.10
4x + 5y = 10.80
4x - 5y = 10.80
4x + 10.80y = 5
Hudson is already 40 miles away from home on his drive back to college. He is driving 65 mi/h. Write an equation that models the total distance y after x hours.
y = 40x + 65
y = 65x + 40
40x + 65y = 105
y - 40 = 65(x - 0)
When Phil started his new job, he owed the company $65 for his uniforms. He is earning $13 per hour. The cost of his uniforms is withheld from his earnings. Write an equation that models the total money he has y after x hours of work.
y = 13x - 65
y = 13x + 65
13x - 65y = -52
y - 65 = 13(x - 1)
A sign says that 3 tickets cost $22.50 and that 7 tickets cost $52.50. Which equations in point-slope form would represents the cost of tickets? Select all that apply.
y - 22.50 = 7.50(x - 3)
y - 52.50 = 7.50(x - 7)
y = 7.50x
y + 22.50 = 7.50(x + 3)
The population of a city increases by 4000 people each year. In 2025, the population is projected to be 450,000 people. What is an equation that gives the city's population y (in thousands of people) x years after 2010?
y = 4x + 450
y - 450 = 4(x - 15)
y - 15 = 4(x - 450)
y = 4x + 15
You have only nickels (x) and dimes (y) in your piggy bank. When you ran the coins through a change counter, it indicated you have 595 cents. Write an equation to represent this situation.
5x + 10y = 595
10x + 5y = 595
.05x + .10y = 595
y = 2x + 595
Two farmers use combines to harvest corn from their fields. One farmer can harvest 600 acres of corn per day, and the other farmer can harvest 1000 acres of corn per day. They harvested 9800 acres of corn total. Which equations could represent this situation? Choose all that apply.
600x + 1000y = 9800
1000x + 600y = 9800
y = 6/10x + 9800
y = 10/6x + 9800
A football team scores 63 points. All of the points come from field goals (x) worth 3 points and touchdowns (y) worth 7 points. Write an equation in standard form that represents this situation. Then convert it to slope-intercept form. Select the correct standard form and slope-intercept form.
3x + 7y = 63
7x + 3y = 63
y=−73x+9
y=−37x+21
The local service center advertises that it charges a flat fee of $50 plus $8 per mile to tow a vehicle. Write an equation that represents the total cost (C) of a service for m miles of towing.
y = 8x + 50
C = 50m +8
y = 50x + 8
C = 8m + 50
Find the equation of the line in the graph.
y = 2x + 5
y = -2x + 5
y = 5 + 2x
y = - x + 5
Bob's Plumbing charges $15 per hour plus a service fee of $40 for coming out to your house. Which equation models this situation?
y = 15x + 40
y = 40x + 15
y = 15x
y = 15x - 40
Dexter's Gym charges a one-time registration fee of $40 and $20 each month. The total fee after x months is $340. Which equation models this situation?
40x + 20 = 340
20x + 40 = 340
20x - 40 = 340
20 + 340 = 40x
Scott's Automotive charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie was charged $63.
35x + 7 = 63
7x = 63
7x - 35 = 63
7x + 35 = 63
A holiday meal cost $12.50 a person plus a delivery fee of $30. Which equation represents the amount a holiday meal costs(y), including delivery, for x people?
y = 12.50 + 30x
y = 30 + 12.50x
y = 12.50 + 30
12.50x = 30
Ace Telecommunications charges $0.12 per minute of phone use plus a monthly service fee of $8.00 for it phone service. Which equation can be used to find c, the total cost for one month when m, minutes are used?
c = 0.12m + 8m
c = 8m + 0.12m
c = 0.12m + 8
c = 0.20m
You are visiting Baltimore, MD and a taxi company charges you a flat fee of $3.00 for using the taxi and $0.75 per mile.
Which of the following equations matches the situation?
0.75x + 3y = 50
y = 0.75x + 3
y = 3x + 0.75
3x + 0.75y = 50
50 = -0.75x + y
A plumber charges $50 to make a house call. He also charges $25 per hour for labor.
How much would it cost for 2.5 hours of labor?
$100
4.50
$112.50
$65.00
$123.45
Your new job is at the Custom T Shop, where T Shirts are printed to order. For each order, Custom T Shop charges $8 per shirt plus a one time set up fee of $15, represented by the equation y=8x+15
How much would 50 shirts cost?
y= 40
y= 400
y= 415
y= 65
y= 390
The rental rate at Rent A Wreck is $30 per day plus $0.25 per mile driven.
How much would a 100 mile rental cost?
$45
$55
$23
$100
4 seconds
-2 seconds
-6 seconds
6 seconds
A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula h t = −16 t2 + 8t + 24, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How high is the platform?
.25 ft
24 ft
25 ft
8 ft
The height of an object thrown into the air can be modeled by the formula y=−16x2+70x+95 , where y is in feet after x seconds.
What is the height of the object after 5 seconds?
95 feet
45 feet
70 feet
171.56 feet
The height of an object thrown into the air can be modeled by the formula y=−16x2+70x+95
, where y is in feet after x seconds.
What is the initial height of the object?
70 feet
95 feet
149 feet
-16 feet
A ball is thrown into the air with an upward velocity. Its height, h, after t seconds is given by the function below.
h=−16t2+64t+960
How many seconds did it take for the ball to reach its maximum height?
10 seconds
64 seconds
960 seconds
2 seconds
Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = –16t2 + 16t + 480, where t is the time in seconds and h is the height in feet. How long does it take Jason to hit the water?
-16 seconds
-6 seconds
0 seconds
6 seconds
Members of the math club launch a model rocket from ground level with an initial velocity of 96 ft/sec. This can be modeled with the function h(t) = -16t2 + 96t. When does the rocket hit the ground?
7 seconds
6 seconds
3 seconds
8 seconds
You jump off a 24 foot high cliff and your fall is modeled by the function:
h(t) = -16t2 + 8t + 24
When would you reach 16 feet above the water?
8 seconds
1 second
1/2 second
1/4 second
If each mark on the x-axis represents one second, when did the object reach the ground?
2.5 seconds
6 seconds
5.5 seconds
5 seconds
An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t2 + 64t + 80
What will be the object's maximum height?
2 ft
80 ft
144 ft
64 ft
You jump off a 24 foot high cliff and your fall is modeled by the function:
h(t) = -16t2 + 8t + 24
How long would it take you to hit the water?
8 seconds
1 second
1.5 seconds
1/4 second
The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:
p= -15x2 +600x +60
What is the maximum profit you can make from selling tickets?
$6060
$20
$600
$10,250
Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:
h = -16t2 + 80
About how long did it take for the balloon to hit the ground?
1.73 seconds
2.24 seconds
2.45 seconds
2.83 seconds
Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.
h = -5t2 + 45
When is the ball at ground level?
only at t = 0 seconds
only at t = 3 seconds
only at t = 9 seconds
at both t = 0 seconds and t = 3 seconds
Jason launched a rocket for a physics experiment. This equation can be used to find the height (h), in feet, of the rocket after t seconds.
h = -16t2 + 288t + 8
How many seconds will it take for the rocket to reach a height of 1,304 feet?
9.0 seconds
9.6 seconds
81.0 seconds
82.0 seconds
You jump off a 24 foot high cliff and your fall is modeled by the function:
h(t) = -16t2 + 8t + 24
When would you reach 16 feet above the water?
8 seconds
1 second
1/2 second
1/4 second
A local sports team models its ticket sales revenue, in thousands of dollars, with the function
f(x) = 5x² +15x -90
where x represents the number of games played. How many games must the team play for its revenue to be $0?
(a)
