1. -17 = y-5
Switch the left and right sides (this is merely for convenience). This gives:
y – 5 = -17
Add 5 to both sides to get:
y – 5 + 5 = -17 + 5
y = -12
2. -6+y= -17
Add 6 to both sides to get:
-6 + 6 + y = -17 + 6
y = -11
3. Use formula to solve the following C = cost, M= markup S= selling price, C+M=S.
The selling price of a computer is $1850. If the markup on the computer is $150, find the
cost to the retailer.
First, subtract “M” from both sides of the given equation to get:
C+M–M=S–M
C=S–M
Then substitute the given values for the selling price, S = 1850, and the markup,
M = 150, and solve for the cost, C:
C = 1850 – 150
C = 1700
4. -28=8z
Switch the left and right sides, again for convenience:
8z = -28
Divide both sides by 8 to get:
z=−
28
8
Simplify the fraction on the right side by dividing both the numerator and the
denominator by 4 to get:
z=−
7
2
5. –x – 3= 3
Add 3 to both sides to get:
-x – 3 + 3 = 3 + 3
-x = 6
Multiply both sides by -1 (Or, equivalently, divide both sides by -1)
(-1)(-x) = (-1)(6)
x = -6
6. Use formula to solve the following: M= n/5 (this is a fraction) m=miles, n= seconds,
If you are 2 miles away from a lightning flash, how long will it take the sound of the
thunder to reach you?
Multiply both sides of the given equation by 5 to get:
5(M) = 5(n/5)
5M = n
n = 5M
Substitute the given value, M = 2, and solve for n:
n = 5(2)
n = 10
The sound of the thunder will take 10 seconds to reach you.
7. 5x+3x-4x =10+2
Combine the terms on the left side by combining the coefficients:
5x + 3x – 4x = 10 + 2
(5 + 3 – 4)x = 10 + 2
4x = 10 + 2
Combine the constant terms on the right side to get:
4x = 12
Divide both sides by 4 to get:
x = 12 / 4
x=3
8. 4(x+1)=20
Divide both sides by 4 to get:
x + 1 = 20 / 4
x+1=5
Subtract 1 from both sides to get:
x+1–1=5–1
x=4
9. Speeding fines are determined by the formula: F= 10(x-65) +50,
If a fine comes to $250, how fast was that person driving?
Write the given equation, substituting 250 in place of the variable F:
250 = 10(x – 65) + 50
Switch the left and right sides for convenience:
10(x – 65) + 50 = 250
Subtract 50 from both sides:
10(x – 65) + 50 – 50 = 250 – 50
10(x – 65) = 200
Divide both sides by 10 to get:
10(x – 65) / 10 = 200 / 10
x – 65 = 20
Add 65 to both sides to get:
x – 65 + 65 = 20 + 65
x = 85
The person was driving 85. (No units were given, but mph could be assumed.)
10. d= rt solve for r
Switch the left and right sides for convenience:
rt = d
Divide both sides by t to get:
rt d
=
t
t
r=
d
t
11. I=Prt solve for P
Switch the left and right sides for convenience:
Prt=I
Divide both sides by r to get:
Prt I
=
r
r
Pt =
I
R
Divide both sides by t to get:
Pt I
=
t
rt
P=
I
rt
12. If you are traveling in your car at an average rate of r miles per hour for t hours, then
the distance, d, in miles, that you travel is described by the formula d=rt: distance equals
rate times time.
A. Solve the formula for t
Switch the left and right sides around for convenience to get:
rt = d
Divide both sides by r to get:
rt d
=
r r
t=
d
r
B. Use the formula in part (a) to find the time that you travel if you cover a distance of
100 miles at an average rate of 40 miles per hour
Using the formula from part A, substitute 100 in place of d, and 40 in place of r
and calculate t:
t=
d
r
t=
100
40
t = 2.5
The time of travel is 2.5 hours.
13. A number increased by 60 is equal to 410. Find the number
Let x represent the unknown number.
Increasing that number by 60 can then be represented as x + 60.
Since increasing the unknown number by 60 is equal to 410, we can write the
equation:
x + 60 = 410
To solve this for the value of x, subtract 60 from both sides to get:
x + 60 – 60 = 410 – 60
x = 350
14. According to the American Bureau of labor statistics, you will devote 37 years to
sleeping and watching TV, the number of years sleeping will exceed the number of years
watching TV by 19. Over your lifetime, how many years will you spend on each activity?
Let t represent the number of years spend watching tv.
Since the number of years sleeping will exceed the number of years watching tv
by 19, the number of years sleeping can be represented by the expression t + 19.
Then, since the sum of the years spent sleeping or watching tv will equal 37 years,
we can write the following equation:
t + (t + 19) = 37
To solve this for t, drop the parentheses on the right side and combine the “t”
terms:
t + t + 19 = 37
2t + 19 = 37
Subtract 19 from both sides to get:
2t + 19 – 19 = 37 – 19
2t = 18
Divide both sides by 2 to get:
t = 18 / 2
t=9
This means that the number of years spent watching television is 9 years.
Then, since the number of years spend sleeping is 19 more than the number of
years spent watching television, we can write:
Years spent sleeping = t + 19
Years spent sleeping = 9 + 19
Years spent sleeping = 28
15. A rectangular swimming pool has a width of 25 feet and an area of 2450 square feet.
What is the pools length?
Area is equal to the product of length and width, so we can write the following
equation:
A=L*W
Solve this for the length by dividing both sides by W to get:
A L *W
=
W
W
L=
A
W
Then, substitute the given values for area and width and calculate the length:
L=
2450
25
L = 98
The length of the pool is 98 feet.
16. Which one is of the following is a better buy: a large pizza with a 14 inch diameter
for $12.00 or a medium pizza with a 7 inch diameter for $5.00
For each pizza, calculate the area of the pizza in square inches, and then divide
the cost by the area to get the cost per square inch. Then the cost of each pizza can
be compared.
For the large size pizza:
Area = π r 2
The radius is equal to half of the diameter, so r = 7 inches.
Area = π ( 7 )
2
Area ≈ ( 3.14 ) ( 7 )
2
Area ≈ 153.86in 2
Then, the cost per square inch for the large size pizza is:
Cost per sq. in. =
$12.00
= $0.08 per sq. in.
153.86in 2
For the medium sized pizza:
The radius is equal to half of the diameter, so r = 3.5 inches.
Area = π ( 3.5 )
2
Area ≈ ( 3.14 ) ( 3.5 )
2
Area ≈ 38.465in 2
Then, the cost per square inch for the medium sized pizza is:
Cost per sq. in. =
$5.00
= $0.13 per sq. in.
38.465in 2
Since the cost per square inch for the large pizza is less than the cost per square
inch for the medium pizza, the large pizza is a better buy.
18. a car can be rented for $80 per week plus 25 cents for each mile driven. How many
miles can you travel if you can spend at most $400 for the week
The total cost of the rental is a combination of the fixed cost ($80 per week), and
the per mile cost.
Let x represent the number of miles driven in the week.
The cost of miles driven is equal to 0.25 times the number of miles driven, or
0.25x.
The total cost of the rental is then 80 + 0.25x.
If the most that you can spend is $400, then we can write the following inequality:
80 + 0.25x ≤ 400
Subtract 80 from both sides of the inequality to get:
80 – 80 + 0.25x ≤ 400 – 80
0.25x ≤ 320
Divide both sides by 0.25 to get:
0.25x / 0.25 ≤ 320 / 0.25
x ≤ 1280
The maximum number of miles that you can drive would be 1280.