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 Rs 750. We would like to find out the number of toys produced on that day
Solution:
Let John had x marbles.
Jivanti had 45 - x marbles.
After John lost 5 marbles, the number of marbles he was left with him = x - 5
After Jiavanti lost 5 marbles, the number of marbles she was left with = 45 - x - 5
⇒ 40 - x
Thus, their product = (x - 5) (40 - x)
⇒ 40x - x2 - 200 + 5x
⇒ - x2 + 45x - 200
Given that the product of the marbles they had now is 124.
⇒ - x2 + 45x - 200 = 124
By subtracting 124 from both sides.
⇒ - x2 + 45x - 324 = 0
⇒ x2 - 45x + 324 = 0
The quadratic equation below satisfies the number of marbles John had and is the required mathematical representation of the problem.
x2 - 45x + 324 = 0
(ii) Let x be the number of toys produced in a day.
⇒ The cost of production of each toy on the day = Rs 55 - x
Therefore, The total cost of production that day = Rs x (55 - x)
⇒ x (55 - x) = 750
⇒ 55x - x2 = 750
⇒ - x2 + 55x - 750 = 0
⇒ x2 - 55x + 750 = 0
The quadratic equation below satisfies the number of toys produced that day and is the required mathematical representation of the problem.
x2 - 55x + 750 = 0
☛ Check: NCERT Solutions for Class 10 Maths Chapter 4
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 Rs 750. We would like to find out the number of toys produced on that day
Summary:
The required mathematical representation of the number of marbles John and Jivanti had and the number of toys produced is x2 - 45x + 324 = 0 and x2 - 55x + 750 = 0 respectively
☛ Related Questions:
visual curriculum