Practice Test on Word Problems on Linear Equations

This math practice test on word problems on linear equations in one variable help the students to practice more.

I. Solve the following equations:

1. x/2 - 1/2 = x/3 + 1/4

2. x - (x - 1)/2 = 1 - (x - 2)/3

3. (3x - 2)/3 + (2x + 3)/3 = x + 7/6

4. 2y - 3(y + 1) = 5y - 7

5. 15(y - 4) - 2(y - 9) + 5(y + 6) = 0

6. (4y - 3)/4 - 3 = (5y - 7 )/3 - 4y - 1

7. 4(3y + 2) - 5(6y - 1) = 2(y - 8) - 6(7y - 4) + 4y

8. 0.16(5y - 2) = 0.4y + 7

9. 3x/4 - (x - 1)/4 = (x - 2)/3

II. Problems on linear equations:

1. If 3 is subtracted from seven times a number, the result is 53. Find the number.

2. Find two numbers such that one exceeds the other by 11 and their sum is 73.

3. The sum of three consecutive multiples of 5 is 555. Find the multiples.

4. Three-fourth of a number is more than one-fourth of a number by 2. Find the number.

5. Divide 22 into two parts in such a way that 2/3 of one part is equal to 1/4 of the other.

6. Two numbers are such that the ratio between them is 5 : 2. If each is increased by 1 the ratio between the new numbers so formed is 7 : 3. Find the original number.

7. Three numbers are in the ratio 2 : 3 : 4 and their sum is 54. Find the number.

8. The sum of three consecutive even numbers is 54. Find the numbers.
[Hint: Take the numbers 2x, 2x + 2, 2x + 4]

9. The difference between two positive integers is 32. The ratio of these integers is 1 : 3. Find these integers.

10. The numerator of a fraction is 5 less than the denominator. If 2 is added to both numerator and denominator, it becomes 4/5. Find the fraction.

11. The numerator of a fraction is 1 less than the denominator. If numerator is decreased by 2 and denominator is increased by 3, the fraction becomes 1/4. Find the fraction.

12. The sum of the digits of a 2 digit number is 8. The number obtained by interchanging the digits exceeds the original number by 18.

13. A number consists of two digits whose sum is 5. If 9 is subtracted from the number the digits are reversed. Find the number.

14. A number consists of two-digits. The digit at the units place is 3 times the digit at the tens place. If 36 is added to the number, the digits are reversed. Find the number.

15. The present ages of Andy and Mike are in the ratio 5 : 3. If Andy had been 7 years older and Mike 7 years younger, the age of Andy would have been 3 times the age of Mike. Find their present ages.

16. Father’s age is three times his son’s age. Four years ago, he was 4 times his son’s age. Find their present ages.

17. A motorboat goes downstream in the river and covers the distance between two coastal town in 3 hours. It covers this distance upstream in 4 hours. If the speed of the stream is 5 km/hr, find the speed of the boat in still water and the distance between the two coastal towns.

18. A boat travels 20 km upstream in a river in the same period of time as it takes to travel 30 km downstream. If the rate of the stream is 4 km/hr, find the speed of boat in still water.

19. The length of the rectangle is 4 times its width. If the perimeter of the rectangle is 80 m, find the length and breadth of rectangle.

20. Length of rectangle is 4 m less than 3 times its breadth. If the perimeter of rectangle is 32 m. Find its length and breadth

Answers for the practice test on word problems on linear equations in one variable are given below to check the exact answers.

Answers:

I. 1. 9/2

2. 7/5

3. 5/4

4. 2/3

5. 2/3

6. 1/8

7. -5/18

8. 18.3

9. -11/2

II. 1. 8

2. 31, 42

3. 180, 185, 190

4. 4

5. 6, 16

6. 20, 8

7. 12, 18, 24

8. 16, 18, 20

9. 16, 48

10. 18/23

11. 4/5

12. 35

13. 32

14. 26

15. 35 years, 21 years

16. 12 years, 36 years

17. 35 km/h, 120 km

18. 20 km/h

19. length = 32 m, breadth = 8 m

20. length = 11 m, breadth = 5 m.