Study Island
Copyright © 2015 Edmentum - All rights reserved.
Generation Date: 02/22/2015
Generated By: Robert Dilliplane
1. A rental car company charges a base fee of $42.48 plus $0.50 per mile driven. If x represents
the number of miles driven, which of the following equations could be used to find y, the total
cost of the bill?
A. y = $42.98x
B. y = $0.50x + $42.48
C. y = $42.48x + $0.50
D. y = $0.80x + $42.48
2. When Jonas does his math homework, he spends an average of 4 minutes on each problem.
Last night he spent 1.2 hours on his non-math homework, plus he completed 5 math problems.
Approximately how much time did Jonas spend in total on all of his homework last night?
A. 2.4 hours
B. 1.5 hours
C. 1 hours
D. 1.9 hours
3. A company manufactures and sells mini-recorders. A survey of office supply stores indicated
that the demand for 4 hundred recorders would cause them all to be sold if they cost $70 each,
and the demand for 9 hundred recorders would cause them all to be sold if they cost $30 each. If
a linear relationship between demand and price exists, which of the following equations models
the demand-price relationship?
(Let x represent the demand in hundreds and y represent the price per mini-recorder.)
A. y = 8(x)
B. y = -8(x) + 102
C. y = 4(x) + 66
D. y = -8(x) + 78
4. LeAnne leaves town traveling at an average speed of 47 mph. After 3 hours, Bart leaves town
traveling in the same direction at an average speed of 65 mph. Which of the following equations
could be used to represent the distance between LeAnne and Bart after x hours?
(Let x represent the time in hours that Bart has been traveling and y represent the distance
between LeAnne and Bart.)
A. y = 141 - 18x
B. y = 141 + 18x
C. y = 18x
D. y = 141 - 65x
5. Jodie pulls into the local convenience store to fill her car up with gas. The 89-octane gas is
selling for $1.99 a gallon. She uses the pay at the pump feature and decides to get her car washed
for an extra $4.00. What is the total amount of her purchase if she gets 10 gallons of gas?
A. $23.90
B. $19.90
C. $26.40
D. $24.90
6. The Bedrock water department has a monthly service charge of $8.50 and a volume charge of
$2.25 for every 100 cubic feet of water. Which of the following equations can be used to
determine the Sandstone family's monthly water bill?
(Let x represent 100 cubic feet of water and y represent the monthly cost.)
A. y = 10.75x
B. y = 2.25x + 8.50
C. y = 0.0225x + 8.50
D. y = 2.25x - 8.50
7.
A.
B.
C.
D.
8. A radio station gave away concert tickets every hour yesterday. At the end of the fourth hour,
the station had 220 tickets left. At the end of the eighth hour, the station had 176 tickets left.
Write an equation in general form that expresses the number of tickets left at the radio station, y,
as a function of the number of hours past, x.
A. 11x - y = 264
B. 11x + y = 264
C. 11x - y = -88
D. 11x + y = 88
9. Solve for x.
A.
B.
C.
D.
10. Mike discovered that the pool in his backyard is leaking slowly. The pool holds 14,225
gallons of water, and is leaking at a rate of 10 gallons per day. If Mike does not replace the water
that has leaked from the pool, how many gallons of water will remain in the pool after 132 days?
A. 15,545 gallons
B. 13,565 gallons
C. 12,905 gallons
D. 14,357 gallons
11. Betsy's high school is putting on a production of a play as a fundraiser for the school's music
programs. A local bank has agreed to allow the school to use a line of credit from which they can
withdraw money to pay for the play. Then, any deposits they make at the bank will be applied to
the negative balance of the credit account.
The play cost $2,600.00 to produce, and they intend to sell tickets for $9 each. After the play,
Betsy will take the ticket proceeds and deposit them with the bank. If 839 people attend the
play's opening night, what will the balance of the bank account be?
A. $7,551
B. - $2,507
C. $4,951
D. $10,151
12. Forrest Lumber uses the function
S(t) = -120t + 960
to determine the salvage value, S(t), in dollars, of a table saw t years after its purchase. How long
will it take the saw to depreciate completely?
A. 6 years
B. 8 years
C. 10 years
D. 9 years
Answers
1. B
2. B
3. B
4. A
5. A
6. B
7. C
8. B
9. B
10. C
11. C
12. B
Explanations
1. The total bill is equal to the cost per mile driven, $0.50, times the number of miles driven, x,
plus the base price, $42.48. Therefore, the linear equation which represents the total rental cost is
shown below.
y = $0.50x + $42.48
2. This situation can be represented by a linear equation where the total homework time is the
dependent variable and the number of math problems is the independent variable.
The time spent on non-math homework is the y-intercept, and the time per math problem is the
rate of change, or slope.
First, convert the time per math problem from minutes to hours. Since one problem takes 4
minutes, that is equivalent to
hours.
Use the given information to develop an equation and solve for the total homework time.
Jonas spent about 1.5 hours on his homework last night.
3. Let y represent the price per mini-recorder and x represent the demand in hundreds. The
problem gives us two points and indicates that the demand-price function is linear. Given any
two points we should be able to find the equation of the line passing through the points.
So, given the points (4, 70) and (9, 30), find the slope.
m = (y2 - y1)/(x2 - x1) = (30 - 70)/(9 - 4) = -40/5 = -8
Now that we have the slope, use the slope-point form of the equation of a line to find the
demand-price function.
y - y1 = m(x - x1)
y - 70 = -8(x - 4)
y = -8x + 32 + 70
y = -8(x) + 102
4. First, find the distance that LeAnne has already traveled since she left town.
47 mph · 3 hours = 141 miles
Next, find the speed at which Bart is approaching LeAnne.
65 mph - 47 mph = 18 mph
Next, find an equation that represents the distance between LeAnne and Bart.
y = 141 - 18x
5. Let y represent the total amount of her purchase and x represent the number of gallons of gas.
y(x) = (cost per gallon)x + car wash
y(x) = ($1.99/gallon)(x gallons) + $4
Since she purchased 10 gallons of gas, her total purchase cost is shown below.
y(10) = ($1.99/gallon)(10 gallons) + $4 = $23.90
6. The monthly cost is equal to the volume charge plus the service charge.
monthly cost = volume charge + service charge
y = 2.25x + 8.50
7.
8. Each pair of time and ticket values can be written as a point.
Use the points to find the slope of the function.
Substitute the slope and one of the points into the point-slope formula.
9. Solve for x.
10. The amount of water in the pool can be modeled by the linear equation below, where V
represents the amount of water in the pool and t represents the the time that has passed in days.
Evaluate the equation with the given time frame to determine the amount of water in the pool.
11. The balance in the bank account can be modeled by the linear equation below, where B
represents the balance of the account and p represents the number of people in attendance at the
play.
Evaluate the equation with the given attendance figure to determine the balance of the bank
account.
12. The saw is completely depreciated when S(t) = 0. So, set S(t) = 0 and solve for t.
0 = -120t + 960
120t = 960
t=8
Therefore, it will take 8 years for the saw to depreciate completely.