Solve the problems given in Example 1
Solution:
The problem in example 1 was as follows:
Represent the following situations mathematically:
(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.
(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. We would like to find out the number of toys produced on that day.
Given:
(i) Let the number of marbles that John had be x.
The number of marbles Jivanti had will be = 45 - x
Both of them lost 5 marbles each:
Marbles with John = x - 5
Marbles with Jivanti = 45 - x - 5 = 40 - x
Product of current number of marbles = 124
Let us use this condition to form a quadratic equation.
(x - 5) (40 - x) = 124
(i) (x - 5) (40 - x) = 124
⇒ 40x - x2 - 200 + 5x = 124
⇒ -x2 + 45x - 200 -124 = 0
⇒ -x2 + 45x - 324 = 0
On multiplying both sides of the equation with negative sign, we get
⇒ x2 - 45x + 324 = 0
⇒ x2 - 36x - 9x + 324 = 0
⇒ x(x - 36) - 9 (x - 36) = 0
⇒ (x - 36) (x - 9) = 0
⇒ x - 36 = 0 and x - 9 = 0
⇒ x = 36 and x = 9
John and Jivanti started with 36 and 9 marbles.
(ii) Let the number of toys produced in a day be x.
Cost of each toy = (55 - x) rupees
Total cost of production = cost of each toy × Total number of toys
⇒ (55 - x) (x) = 750
⇒ 55x - x2 = 750
⇒ 55x - x2 - 750 = 0
⇒ x2 - 25x - 30x + 750 = 0
⇒ (x - 25) (x - 30) = 0
x - 25 = 0 and x - 30 = 0
x = 25 and x = 30
The number of toys produced on that day is 25 or 30.
☛ Check: NCERT Solutions Class 10 Maths Chapter 4
Video Solution:
Solve the problems given in example 1
Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.2 Question 2
Summary:
If John and Jivanti together have 45 marbles and both of them lost 5 marbles each, and the product of the number of marbles they now have is 124 then the number of marbles they had to start with is 9 and 36.
If a cottage industry produces a certain number of toys in a day and the cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day where, on a particular day, the total cost of production was ₹ 750, the number of toys produced on that day is 25 or 30.
☛ Related Questions:
- Find two numbers whose sum is 27 and product is 182.
- Find two consecutive positive integers, the sum of whose square is 365.
- The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
- A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs.90, find the number of articles produced and the cost of each article
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