8th Grade Math Unit 3 - Solve Linear Equations

Which equation below represents the perimeter, P, of the following figure?

Review Solving Equations
1. P=L • W
2. P = L + W
3. P = 2 ( L + W )
4. P = 2 ( L • W)
What is the total area of the surfaces of this figure, if the measurements shown are in ft.:

__________ sq. ft.
What would the area of a rectangular box be if the width is s, the height is 2s, and the length is 5s.
1. A = s • 2s • 5s
2. A = 2(s • 5s) + 2(s • 2s) + 2(5s • 2s)
3. A = 20s + 4s
4. A = s + 2s + 5s
Your Dad is going on a diet. He weighs 190 pounds today. His goal is to weigh 175 pounds. Which equations below represent the amount of weight he has to lose?

Check all that apply.
1. L = 175 - 190
2. L = 190 - 175
3. 190 - L = 175
4. 175 + L = 190
5. 175 = 190 - L
Which equation below represents:

Half the sum of eight and x is the same as x minus 4.
1. 1/2 (8 + x) = 4 - x
2. 1/2(8) + x = x - 4
3. 1/2 (8 + x) = x - 4
4. 1/2(8) + x = 4 - x
The equation for:

three sevenths the square of the sum of x, y and z equals the sum of the square of x and the square of z

is:

3/7 (x + y + z)² = x² + z²
1. True
2. False
You are wiring your bedroom for a stereo. Speaker cable costs $ 1.25 per foot. You buy x feet of speaker wire and pay $ 4.85 in tax. If your total cost is $84.90, which equation below represents the situation?
1. x ( 1.25 + 4.85) = 84.90
2. x = 84.90 - (1.25 • 4.85)
3. (x • 1.25) + 4.85 = 84.90
4. (x • 1.25) = 84.90 + 4.85
Your dog weighs y pounds. Your sister weighs y + 8 pounds.

Which story below fits this equation:

3y + (y + 16) = 179
1. Three times your dog's weight plus eight pounds more than your sister's weight equals one hundred seventy nine pounds.
2. Three times the sum of your dog's weight and your sister's weight plus eight more pounds equals 179 pounds.
During a 60 minute class, the teaching portion lasted 3 times the announcements portion. If x represents the time for the announcements, write an expression for the teaching portion.

Check the correct expression.
1. 60 = x + 3x
2. x = 60 + 3x
3. 3x - x = 60
4. 3x = 60 + x
The volume of a sphere is four thirds times π times the radius r of the sphere cubed. If r = 3 inches, what is the volume?

(First write the equation for the volume, V, of the sphere. Then solve for V with r = 3, and π = 3.14).

V = ___________ cu. in.
Solve for m:

- 5 = m + ( - 4.32)

m = ________
Write the equation and then solve:

The sum of 29 and 32 and a number is equal to 98. What is the number?
Your Mom drives a practical 4-cylinder mid-size car that gets 12 miles more per gallon than your Dad's 8-cylinder SUV. A mid-size car gets 32 miles per gallon. You are going to be driving a 3-cylinder sub-compact car that will get 17 miles more than your Dad's SUV on one gallon of gas. How far will you be able to go on one gallon of gas?

______________ miles
Your 80 year-old grandmother is 63 inches tall. When she was 21 years old, she was 66 inches tall. How many inches of height has she lost?

_______ inches
Which equation is not equivalent to:

x - 14 = 38
1. x + 7 = 59
2. x = 52
3. x - 14 = 40
4. x - 13 = 39
Check the solutions below that are correct.

Check all that apply.
1. - 5.63b = 87.265
  b = - 15.5
2. - 7y = - 4 2/3
  y = - 2/3
3. ( - 2 3/5 ) m = - 33
  m = 12 9/13
A study shows that one ninth of the students in your school were born in New York. If 28 students were born in New York, how many students are in your school?

___________ students
If 5a - 8 = 7, what is the value of 22a - 14?
The rectangle below is divided into six squares. If the perimeter of the rectangle is 70 inches, what is the area of each square?

Area = _________ sq. in.
Check the solutions below that are correct.

Check all that apply.
1. - 2.5b - 43.6 = 64.9
  b = 43.4
2. (8x +3)/4 - 8 = 6.2
  
  x = 6.725
3. The smallest of three consecutive even integers whose sum is -42 is:
  
  - 16
4. The equation used to find four consecutive odd integers whose sum is 8 is:
  
  n+1 + n+2 + n+4 + n+6 = 8
Dillon received his allowance from his Dad. He spent one third of the money on a movie. He then spent half of what was left on lunch. He spent $7.85 on a baseball. When he got home he had $ 2.15 left. How much did he receive for his allowance?

$ ___________
The sum of two consecutive even numbers equals the sum of two consecutive odd numbers.
1. Always true
2. Never true
3. Sometimes true
Which equation has the solution of - 6?
1. 3a - 6 = 4
2. (4a - 7)/4 = 3
3. 3a + 8 = 7
4. (2/3) • a + 29 = 25
Solve for b:

9.42 + 7.7b = 51.77

b = _________
Check which solutions below are correct:

(Check all that apply.)
1. 4b - 8 = - 6b + 9
  
  b = 1.7
2. (3/4)x + 18 = 4 - (1/8)x
  
  x = 16
3. 7 - 1/2(a - 4) = 11
  
  a = - 4
4. 2.35m - 7 = - 1.55m + 7.625
  
  m = 3.75
5. -4(3y - 7) = 0.25( - 16y + 20)
  
  y = 8/23
Which equation below correctly expresses the following:

three times the greatest of three consecutive even integers exceeds twice the least by 38
1. 3(n + 4) = 2n - 38
2. 3n + 38 - 2(n + 4)
3. 3(n + 4) = 2n + 38
4. 3(n + 4) + 38 = 2n
The side of a square is 4x. One side of a rectangle is 4x + 1, and the other side is x.
Draw and label these figures. If both figures have the same perimeter, what is x?
1. 2/3
2. 1
3. - 1/3
4. 3
Is there a solution to the following?

5m + 4 = 7(m + 1) - 2m
1. Yes
2. No
3. Sometimes
Check which of the following pairs of ratios form a proportion:

(Check all that apply.)

Review Ratios and Proportions
1. 3/2, 24/16
2. 3.1/4.5, 5.2/7.1
3. 0.5/1.5, .4/1.2
4. 42.2/16.4, 28.6/12.6
Solve the following proportion. Write you answer to the nearest hundredth.

0.7/2.3 = x/8.4

x = ________
Which ratio is not equal to 12/15
If a/b = 3/4; and b/c = 4/5, then solve for c if a = 12

c = _______
Check the correct answers below. Both the percentage amount and increase/decrease designation must be correct. Round all percents to the nearest whole percent.
1. Original: 20
  New: 25
  
  25% increase
2. Original: 69
  New: 48
  
  44% decrease
3. Original: 14.7
  New: 12.6
  
  14% decrease
4. Original: 15.6
  New: 28.7
  
  84% increase
A DVD player is listed for sale at $129.95. The store is offering 25% off (a 25% discount). The sales tax is 6.5%.
What will be your total bill when you check out?

Write your answer to the nearest penny.

$_____________
A tree in your back yard grew from 128 inches to 179 inches. Which proportion below represents the rate of change?
1. 128/179 = r/100
2. 51/179 = r/100
3. 51/128 = r/100
4. r/128 = 51/100
Solve the following equation for n:

(2/3)n + x = y
1. n = (3/2)y - x
2. n = (y - x)(2/3)
3. n = (3/2)(y - x)
4. n = (2/3) (x - y)
Solve the following for m:

Three fourths of a number n is 4 more than one half of another number m.

m = ________
1. m = (3/4) n + 4
2. m = 2n - 4
3. m = (3/2)n - 4
4. m = (2/3)n + 4
The area of a trapezoid is:

A = (1/2) h (a + b), where h is the height, a is the top base, and b is the bottom base.

What is the height of a trapezoid with an area of 32 square feet, and bases of 6 feet and 10 feet?

h = _________ ft.
What is the area of a triangle with a base of 24 inches and a height of 10 inches.

Area = __________ sq. in.
You have a bracelet that needs to replated with an alloy of gold and silver. Gold costs $800 per oz. and silver costs $20 per ounce. The jeweler tells you that it will take 12 oz. of alloy to replate your watch. He wants to know how much gold he should use in the alloy. You tell the jeweler that you can afford an alloy that costs $300 per oz. How much gold will he use in the alloy. Let g represent the amount of gold used in the alloy.

_____ oz. ( Write your answer to the nearest tenth of an oz.)
Your teacher says that a test grade is worth 4 times as much as a quiz grade. Your quiz grades are: 85, 87, 93. and 82. Your test grades are 90, and 88. What is your average?

Write your answer to the nearest whole number.

Review Weighted Averages
Two cars leave Charlotte at the same time and travel in opposite directions along I- 77. One car travels 14 miles per hour faster than the other car. After four hours they are 480 miles apart. What is the speed of the slower car? Remember: Distance = speed x time.

________ mph