IBEW Aptitude Test Solving Linear Equations 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?

Accepted Answer

7 feet

Answer

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?

Accepted Answer

$70/hr

Answer

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)?

Accepted Answer

z = 23/3

Answer

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

Accepted Answer

x = 20

Answer

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?

Accepted Answer

10 inches

Answer

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.

IBEW - Aptitude Test Practice Test

IBEW - Aptitude Test Practice Test

IBEW Aptitude Test Solving Linear Equations Questions and Answers