IBEW Aptitude Test Solving Linear Equations Questions and Answers — Questions and Answers
Question 1: An electrician has a 50-foot stick of conduit. They cut 6 identical pieces from it for a job and have 8 feet of conduit left over. What is the length of each piece that was cut?
- 6 feet
- 7 feet (Correct answer)
- 8 feet
- 8.33 feet
Correct answer: 7 feet
Let 'x' represent the length of each identical piece. The total length of the 6 pieces is 6x. The original length was 50 feet, and 8 feet remain. The equation is 50 - 6x = 8. To solve for x, subtract 50 from both sides to get -6x = -42. Then, divide both sides by -6 to find x = 7. Each piece is 7 feet long.
Question 2: An electrical contractor charges a flat $75 service fee plus an hourly rate for labor. If a job takes 4 hours and the total bill is $355, what is the contractor's hourly rate?
- $65/hr
- $88.75/hr
- $70/hr (Correct answer)
- $80/hr
Correct answer: $70/hr
Let 'x' be the hourly rate. The total cost can be represented by the equation: Total Bill = Service Fee + (Hours × Hourly Rate). Plugging in the given values: $355 = $75 + 4x. First, subtract the $75 service fee from both sides: $355 - $75 = 4x, which gives $280 = 4x. Then, divide by the 4 hours of labor to find the hourly rate: x = $280 / 4 = $70.
Question 3: Which of the following is the correct solution for 'z' in the equation 5(z - 2) - 3 = 2(z + 5)?
- z = 9
- z = 23/3 (Correct answer)
- z = 1
- z = 11/3
Correct answer: z = 23/3
First, apply the distributive property to both sides: 5z - 10 - 3 = 2z + 10. Combine the constant terms on the left side: 5z - 13 = 2z + 10. Next, get the variable terms on one side by subtracting 2z from both sides: 3z - 13 = 10. Then, add 13 to both sides: 3z = 23. Finally, divide by 3 to get z = 23/3.
Question 4: Find the value of x that solves the following equation: (1/2)x + 5 = (3/4)x
- x = 20 (Correct answer)
- x = 15
- x = 10
- x = -10
Correct answer: x = 20
To eliminate the fractions, multiply the entire equation by the least common denominator, which is 4. This gives: 4((1/2)x) + 4(5) = 4((3/4)x). The equation simplifies to 2x + 20 = 3x. To isolate x, subtract 2x from both sides, which results in x = 20.
Question 5: The perimeter of a rectangular electrical panel is 54 inches. The length of the panel is 3 inches less than twice its width. What is the width of the panel?
- 12 inches
- 9 inches
- 17 inches
- 10 inches (Correct answer)
Correct answer: 10 inches
Let 'W' be the width and 'L' be the length. We are given L = 2W - 3 and the perimeter P = 54. The perimeter formula is P = 2(L + W). Substitute the expressions for P and L: 54 = 2((2W - 3) + W). Simplify inside the parentheses: 54 = 2(3W - 3). Distribute the 2: 54 = 6W - 6. Add 6 to both sides: 60 = 6W. Finally, divide by 6 to find the width: W = 10 inches.
Question 6: Solve the following linear equation for y: 7y - 11 = 3y + 5
- y = 2
- y = 1.6
- y = -4
- y = 4 (Correct answer)
Correct answer: y = 4
To solve for y, first move the variable terms to one side. Subtract 3y from both sides: 7y - 3y - 11 = 5, which simplifies to 4y - 11 = 5. Next, move the constant terms to the other side by adding 11 to both sides: 4y = 5 + 11, which gives 4y = 16. Finally, divide both sides by 4 to get y = 4.
IBEW Aptitude Test Solving Linear Equations Questions and Answers
An electrician has a 50-foot stick of conduit.
They cut 6 identical pieces from it for a job and have 8 feet of conduit left over.
What is the length of each piece that was cut?