PRACTICE PROBLEMS ON SOLVING LINEAR EQUATIONS

Word Problems on Solving One Step Equations

1) Eighteen more than the number n is 125. What is the value of n?

2) Jim’s three fish tanks contain an equal amount of fish. If Jim has a total of 27 fish, how many fish are in each tank?

3) Steven went to the store and bought five sweatshirts. He spent $45. What was the price of each shirt?

4) How many boxes of envelopes can you buy with $12, if one box costs $3?

5) At a restaurant, Bill and his four friends decided to divide the bill evenly. If each person paid $12, what was the total bill?

6) Last Saturday, Allyson had $38. For her birthday she received more money. She now has $90. How much money did she receive?

7) The sum of three fourths of the number a and 24 is negative 9. What is the value of a?

8) Twenty is 7 less than twice the number w. What is the value of w?

9) -11+ x = 9

Given the above equation, what is the value of 20-(11-x) ?

10) Two and three fifths of a number equals -26. What is the number?

Solution

Answers :

1) n = 107

2) x = 9

3) x = 9

4) x = 4

5) $60

6) x = $52

7) a = -44

8) w = 13.5

9) 29

10) x = -10

Word Problems on Solving Two Step Equations

1) The sum of three times a number x and 5 is 17. What is the number?

2) As a membership fee, a health club charges a one-time amount of $40 and charges $25 for each month. The total fee after m months is $240. What is the value of m?

3) A runner warms up for ten minutes and then takes seven minutes to run each mile. The total time after r miles is 45 minutes. How many miles are run?

4) Jaimie picks out a blouse to purchase. It is on sale for 25% off plus she has got $10 off coupon. She pays $23 for the blouse. Determine the original price.

5) Michael is collecting sea glass from the beach. He begins with 14 pieces in his collection and adds 3 new pieces per day. Determine how many days it will take Michael to have 80 pieces of sea glasses in his collection.

6) Jacob joined a gym last year. His total bill for the year was $410 including a monthly membership fee and a one-time $50 enrolment fee.

7) The cell phone company charges $44.95 a month and $0.25 per text message. The bill for the month is $60.45. How many texts (x) were sent?

Solution

Answers :

1) x = 4

2) m = 8

3) r = 5

4) x = 44

5) x = 22

6) x = 30

7) x = 62

Word Problems on Solving Linear Equations

1) The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.

2) The sum of three consecutive odd natural numbers is 69. Find the prime number out of these numbers.

3) The sum of three consecutive numbers is 156. Find the number which is a multiple of 13 out of these numbers.

4) Divide 54 into two parts such that one part is 2/7 of the other.

5) Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

6) Two equal sides of a triangle are each 4m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55m.

7) After 12 years, Kanwar shall be 3 times as old as he was 4 years ago. Find his present age.

8) If 1/2 is subtracted from a number and the difference is multiplied by 4, the result is 5. What is the number ?

9) The sum of four consecutive integers is 266. What are the integers ?

10) Find a number whose fifth part increased by 30 is equal to its fourth part decreased by 30.

Solution

Answers :

1) 18

2) 23

3) 52

4) 42 and 12

5) 56

6) 9m, 23m and 23m

7) 12 year

8) x = 7/4

9) 65, 66, 67, 68

10) x = 1200

Problem 1 :

Sum of two numbers is 50 and their difference is 10, then the numbers are

(a) 30 and 20 (b) 24 and 14 (c) 12 and 2 (d) none of these

Solution

Problem 2 :

The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digit exceeds the given number by 18, then the number is

(a) 72 (b) 75 (c) 57 (d) none of these

Solution

Problem 3 :

The sum of a two-digit number and the number obtained by interchanging its digit is 99. If the digits differ by 3, then the number is

(a) 36 (b) 33 (c) 66 (d) none of these

Solution

Problem 4 :

Seven times a two-digit number is equal to four times the number obtained by reversing the order of its digit. If the difference between the digits is 3, then find the number.

(a) 36 (b) 33 (c) 66 (d) none of these

Solution

Problem 5 :

A two-digit number is 4 more than 6 times the sum of its digit. If 18 is subtracted from the number, the digits are reversed. Find the number.

(a) 36 (b) 46 (c) 64 (d) none of these

Solution

Problem 6 :

The sum of two numbers is 1000 and the difference between their squares is 256000, then find the numbers.

(a) 616 and 384 (b) 628 and 372 (c) 564 and 436 (d) none of these

Solution

Problem 7 :

Five years ago, A was thrice as old as B and ten years later A shall be twice as old as B, then the present age of A is