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 articles produced in a day. On a particular day, the total cost of production was Rs.750. If x denotes the number of toys produced that day, form the quadratic equation to find x.
Answers
No. of toys produced i.e. x can be 30 or 25 and cost of production of each toys i.e. y is 25 or 30 respectively
•let no. of toys produced = x
•let cost of production of each toy =y
•According to question
•y=55-x ___(1)
•also, total cost of production = no. of •toys × cost of each article
•750= xy____(2)
•multiply (1) by x
•xy= 55x-x²
•750= 55x -x²
•x²-55x+750=0
•x²-30x-25x+750=0
•x(x-30)-25(x-30)=0
•(x-30)(x-25)=0
•x=30 or x=25
•if x=30 or if x=25
•y=25 y=30
The value of x is 30 or 25.
Let the number of toys produced be x and the cost of production be equal to y.
Given in the question that the cost of production of each toy was found to be 55 minus the number of articles produced
y = 55 - x ----(1)
The total cost of production = number of toys × cost of each article
750 = xy -----(2)
On multiplying equation (1)by x we get -
xy= 55x-x²
=> 750= 55x -x² {750 = xy}
=> x²-55x+750=0
=> x²-30x-25x+750=0
=> x(x-30)-25(x-30)=0
=> (x-30)(x-25)=0
=> x=30 or x=25
if x=30 , y = 25
if x=25 , y=30