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CBSE Class 10  >  Class 10 Test  >  The Complete SAT Course  >  Test: Linear Equation Word Problems - Class 10 MCQ

Linear Equation Word Problems - Free MCQ Practice Test with solutions,


MCQ Practice Test & Solutions: Test: Linear Equation Word Problems (10 Questions)

You can prepare effectively for Class 10 The Complete SAT Course with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Linear Equation Word Problems". These 10 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 10

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Test: Linear Equation Word Problems - Question 1
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The product of x and y is 36. If both x and y are integers, then what is the least possible value of x - y?

Detailed Solution: Question 1

If xy = 36 and x and y are integers, then x and y are both factors of 36. In order to minimize the value of x - y, we must find the greatest separation between x and y. The greatest separation between a factor pair is 1 - 36 = -35.

Test: Linear Equation Word Problems - Question 2
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If a factory can manufacture b computer screens in n days at a cost of c dollars per screen, then which of the following represents the total cost, in dollars, of the computer screens that can be manufactured, at that rate, in m days?

Detailed Solution: Question 2

We should regard this as a “conversion” prob- lem from m days into a corresponding number of dollars.

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Test: Linear Equation Word Problems - Question 3
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The symbol Ω represents one of the fundamental operators: +, -, ×, or ÷. If (x Ω y) × (y Ω x) = 1 for all positive values of x and y, then Ω can represent

Detailed Solution: Question 3

The simplest approach is perhaps to choose simple values for x and y, like 2 and 3, and see which operator yields a true equation. Since (2 ÷ 3) × (3 ÷ 2) = 1, the answer is D.

Test: Linear Equation Word Problems - Question 4
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On a typical day, a restaurant sells n grilled cheese sandwiches for p dollars each. Today, however, the manager reduced the price of grilled cheese sandwiches by 30% and as a result sold 50% more of them than usual. Which of the following represents the revenue for today’s grilled cheese sandwich sales, in dollars?

Detailed Solution: Question 4

The revenue is equal to the number of items sold times the price per item. If the restaurant typically sells n sandwiches per day, but today sold 50% more, it sold 1.5n sandwiches. If the price p was reduced 30%, today’s price is 0.70p. Therefore, the total revenue is (1.5n)(0.70p) = 1.05np.

Test: Linear Equation Word Problems - Question 5
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Carlos began with twice as much money as David had. After Carlos gave $12 to David, Carlos still had $10 more than David. How much money did they have combined at the start?

Detailed Solution: Question 5

Let x = the number of dollars David had to start.
If Carlos started with twice as much money as David, then Carlos started with 2x dollars. After Carlos gave David $12, Carlos had 2x - 12 dollars and David had x + 12 dollars. If Carlos still had $10 more than David, then
2x - 12 = 10 + x + 12
Simplify: 2x - 12 = x + 22
Add 12: 2x = x + 34
Subtract x: x = 34
Therefore, David started with $34 and Carlos started with 2($34) = $68, so they had $34 + $68 = $102 combined to start.

Test: Linear Equation Word Problems - Question 6
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Due to inflation, the price of a loaf of bread has increased by 5%. How much does the loaf of bread cost now, when its price was $2.40 last year?

Detailed Solution: Question 6

We calculate the price increase as 5% ⋅ $2.40. We have
5% ⋅ 2.40 = 0.05 ⋅ 2.40 = 0.1200 = 0.12
We must add the price increase to the old price.
2.40 + 0.12 = 2.52
The new price is, therefore, $2.52

Test: Linear Equation Word Problems - Question 7
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To complete a job, three workers get paid at a rate of $12 per hour. If the total pay for the job was $180, then how many hours did the three workers spend on the job?

Detailed Solution: Question 7

We denote the number of hours by x. Then the total price is calculated as the price per hour ($12) times the number of workers times the number of hours (3). We obtain the equation
12 ⋅ 3 ⋅ x = 180
Simplifying this yields
36x = 180
Dividing by 36 gives
x = 180/36 = 5
Therefore, the three workers needed 5 hours for the job.

Test: Linear Equation Word Problems - Question 8
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A farmer cuts a 300 foot fence into two pieces of different sizes. The longer piece should be four times as long as the shorter piece. How long is the shorter pieces?

Detailed Solution: Question 8

x + 4x = 300
Combining the like terms on the left, we get
5x = 300
Dividing by 5, we obtain that
x = 300/5 = 60
Therefore, the shorter piece has a length of 60 feet, while the longer piece has four times this length, that is 4 × 60 feet = 240 feet.

Test: Linear Equation Word Problems - Question 9
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If 4 blocks weigh 28 ounces, how many blocks weigh 70 ounces?

Detailed Solution: Question 9

We denote the weight of a block by x. If 4 blocks weigh 28, then a block weighs x = 28/4 = 7

How many blocks weigh 70? Well, we only need to find 70/7 = 10. So, the answer is 10.

Test: Linear Equation Word Problems - Question 10
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If a circle has circumference 4in, what is its radius?

Detailed Solution: Question 10

We know that C = 2πr where C is the circumference and r is the radius. So in this case
4 = 2πr

Dividing both sides by 2π gives
r = 4/2π = 2/π in ≈ 0.63in

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About this Class 10 Practice Test

This test contains 10 MCQs on Linear Equation Word Problems with detailed solutions for each question. It is part of the The Complete SAT Course course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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