Practice the questions given in the worksheet on word problems on quadratic equations by factoring. We know in order to factorize the given quadratic equation we need to break the middle term or by completing square.
1. The difference of two positive integers is 3 and the sum of their squares is 117; find the numbers.
2. The product of two consecutive positive odd integers is 2499. Find the bigger integer.
3. The product of two positive consecutive even integer is 168. Assuming the smaller integer to be x, frame an equation for the statement and find the numbers.
4. For every litre of petrol, one car travels x km and another car travels 5 km more than the first. If the first car uses 4 litres more than the second car in converting 400 km, frame an equation for the statement to find x. What is the value of x?
5. The product of two consecutive integers is 3906. Find the integers.
6. Divide 51 into two parts whose product is 608.
7. At a party, each member gives a gift to the rest. There were 132 gifts given at the party. Find the number of members.
8. A two-digit number is made of two consecutive digits such that the sum of their squares is 4 less than the number. Find the two-digit number.
9. 780 students stand in rows and columns. Each row has equal number of students and each column has equal number of students. If the number of students in each row is 4 more than the number of rows, find the number of students in each row.
10. Find the percent age of a man if his age 40 years hence will become equal to the square of what his age was 32 years ago.
11. Two pipes together can fill a cistern in 11 1/9 minutes. If operated separately, time taken by the first pipe to fill the cistern is 5 minutes more than that by the second. Find the time required individually for each of the pipes to fill the cistern.
12. Mrs Tendon has two sons, one being exactly one year older than the other. At percentage, her age is equal to the sum of the squares of the ages of her sons. If 4 years hence her age becomes five times the age of the elder son then find the percent ages of her sons.
13. In a triangle the measure of the greatest angle is square of the measure of the smallest angle, and the other angle is double of the smallest angle. Find the greatest angle of the triangle.
14. The lengths (in cm) of parallel sides of a trapezium are 2x and 4x 3x - 1, and the distance between the parallel sides is x + 1. If the area of the trapezium be 28 cm^2, find the smaller of the two parallel sides.
15. Area and perimeter of a rectangular field are 2000 sq.m. and 180 m respectively. Find its length and breadth.
16. The base of a triangle exceeds twice its altitude by 1 8m. If the area of the triangle be 360 sq. m., what is its altitude?
17. Five times of a positive integer is less than twice its square by 3. Find the integer.
18. Smith and Johnson together can do a piece of work in 4 days. If they had to work separately, the time taken by Johnson to do the work would be more than that of Smith by 6 days. In how many days can Smith alone do the work?
19. A shopkeeper buys a certain number of books for $720. If the cost per book was $5 less, the number of books that could be bought for $ 720 would be 2 more. Taking the original cost of each book to be $x, write an equation in x and solve it.
Answers for the worksheet on word problems on quadratic equations by factoring are given below.
1. 6, 9
3. x(x + 2) = 168, 12 and 14
4. 400/x - 400/(x + 5) = 4, 20
5. 62, 63 or -62, -63
6. 32, 19
8. 45 or 65
10. 41 years
11. 20 minutes and 25 minutes
12. 4 years, 5 years
14. 6 cm
15. Length = 50m and Breadth = 40 m
16. 15 m
18. 6 days