IBEW: Electrical Training Alliance Aptitude Test Quiz: Solve Linear Systems

4 questions · exam conditions

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Solve Linear SystemsQuestion 1 of 4

An electrician needs to create 500 feet of a wire bundle from two different spools of wire. The wire from spool A weighs 0.2 pounds per foot, and the wire from spool B weighs 0.3 pounds per foot. The final bundle must weigh exactly 120 pounds. How many feet of wire from spool A must be used?

200 feet

250 feet

300 feet

400 feet

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IBEW: Electrical Training Alliance Aptitude Test Quiz

IBEW: Electrical Training Alliance Aptitude Test Quiz: Solve Linear Systems

Practice Solve Linear Systems in IBEW: Electrical Training Alliance Aptitude Test with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Solve Linear Systems, giving you a quick way to practice the rules, question types, and explanations that matter most for IBEW: Electrical Training Alliance Aptitude Test.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

200 feet
250 feet
300 feet (correct answer)
400 feet

Explanation: Let

a

be the length of wire from spool A and

b

be the length from spool B. We can set up a system of two equations:

Total length: $a + b = 500$
Total weight: $0.2a + 0.3b = 120$ We want to find the value of $a$ . We can use substitution. From the first equation, $b = 500 - a$ . Substitute this into the second equation: $0.2a + 0.3(500 - a) = 120$ $0.2a + 150 - 0.3a = 120$ Combine the $a$ terms: $-0.1a + 150 = 120$ Subtract 150 from both sides: $-0.1a = -30$ Divide by -0.1 (which is the same as multiplying by -10): $a = 300$ 300 feet of wire from spool A must be used.

Question 2

Two apprentices, Alex and Ben, are paid a total of $560 for a job. Alex worked 5 more hours than Ben, and their combined hours totaled 35. If they are paid at the same hourly rate, how much did Alex earn?

$16
$240
$280
$320 (correct answer)

Explanation: This is a multi-step problem. First, find the hours worked by each apprentice. Let

A

be Alex's hours and

B

be Ben's hours.

$A + B = 35$
$A = B + 5$ Substitute the second equation into the first: $(B + 5) + B = 35$ $2B + 5 = 35$ $2B = 30 \rightarrow B = 15$ hours. Alex worked $A = 15 + 5 = 20$ hours. Next, find the hourly rate. The total pay for 35 hours is $560. Rate = Total Pay / Total Hours = $560 / 35 hours. To simplify $560/35$ , we can divide both by 7: $80/5 = 16$ . The hourly rate is $16. Finally, calculate Alex's earnings: Alex's earnings = Alex's hours $\times$ hourly rate = $20 \times \$ 16 = $320$.

Question 3

The total length of two pieces of conduit is 18 feet. If three times the length of the shorter piece is 6 feet more than the length of the longer piece, what is the length of the longer piece?

6 feet
9 feet
12 feet (correct answer)
15 feet

Explanation: Let

L

be the length of the longer piece and

S

be the length of the shorter piece. From the problem statement, we can create two equations:

The total length is 18 feet: $L + S = 18$
'Three times the shorter piece ( $3S$ ) is (=) 6 feet more than the longer piece ( $L+6$ )': $3S = L + 6$ Now we solve the system. From equation (1), we can write $S = 18 - L$ . Substitute this into equation (2): $3(18 - L) = L + 6$ $54 - 3L = L + 6$ $54 - 6 = L + 3L$ $48 = 4L$ $L = 12$ The length of the longer piece is 12 feet.

Question 4

What is the $x$ -coordinate of the solution to the system: $\frac{2}{3}x - y = 4$ and $x + \frac{1}{2}y = 1$ ?

-5/2
-3/2
9/4 (correct answer)
3

Explanation: To solve this system, it is easiest to first eliminate the

y

variable. We can modify the second equation so the

y

coefficient is the opposite of the

y

coefficient in the first equation. The first equation has a

-y

term. Multiply the second equation by 2:

2(x + \frac{1}{2}y) = 2(1) \rightarrow 2x + y = 2

Now we have the system:

$\frac{2}{3}x - y = 4$
$2x + y = 2$ Add the two equations together: $(\frac{2}{3}x - y) + (2x + y) = 4 + 2$ $\frac{2}{3}x + 2x = 6$ To add the $x$ terms, find a common denominator: $2x = \frac{6}{3}x$ . $\frac{2}{3}x + \frac{6}{3}x = 6$ $\frac{8}{3}x = 6$ To solve for $x$ , multiply both sides by the reciprocal of $\frac{8}{3}$ , which is $\frac{3}{8}$ . $x = 6 \times \frac{3}{8} = \frac{18}{8} = \frac{9}{4}$ .