please follow
2. Solve the problems given below.
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.
Answers
Answer:
Step-by-step explanation:
Given John and jivanti together have 45 marbles
Let the number of Marbles John had be= x
Then the number of marbles jivanti had= 45-x
Both of them lost 5 Marbles each
Therefore, the number of marbles John had= x-5
The number of marbles jivanti had= 45-x-5= 40-x
Now product of the number of Marbles =124
Therefore , (x-5)(40-x)=124
40- x²-200+5x=124
-x²+45x-200-124=0
x² -45x+324=0. (Multiplying by(-1))
By factorisation method
x²-36x-9x+324=0
x(x-36) - 9(x-36)=0
(x-36)(x-9)=0
x=36 or x= 9
When John has 36 Marbles and jivanti has = 45-x= 45-36=9 marbles
When John has 9 Marbles and jivanti has= 45-x= 45- 9= 36 marbles
ii) Let the number of toys produced on that day be x.
Therefore the cost of production of each toy that day= 55 - x
So the total cost production that day=number of toys× cost of production of each toy that day
Total cost of production of toy=
x × (55-x)
A.T.Q..
x(55-x)=750
55x -x²= 750
-x²+55x-750=0
x²-55x+750=0
x²- 30x -25x+750=0
x(x-30)-25(x-30)=0
(x-30)(x-25)=0
x-30=0
x=30
x-25=0
x=25
Hence, the number of toys produced= x=25 or 30
Answer:
please follow
2. Solve the problems given below.
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.