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# Solve the following situations mathematically:

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.

Given:

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. $750$.

To do:

Here, we have to find out the number of toys produced on that day.

Solution:

Let the number of toys produced in a day be $x$.

This implies,

The cost of production of each toy $= 55 - x$

The total cost of production is the product of the number of toys produced in a day and the cost of production of each toy $ =x (55 - x)$

Therefore,

$x(55-x) = 750$

$55x-x^2 = 750$

$x^2-55x+750 = 0$

$x^2-25x-30x+750=0$

$x(x-25)-30(x-25)=0$

$(x-25)(x-30)=0$

$x-25=0$ or $x-30=0$

$x=25$ or $x=30$

The number of toys produced on that day was 25 or 30.

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