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.

Related Articles 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 $x$.
Solve 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.
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.
On a rainy day, 94 percent of the students were present in a school. If the number of students absent on that day was 174, find the total strength of the school.
The total number of lotuses in a lake grows in such a way that their number increases twice the previous day. For e.g. If there are \( x \) lotuses on 1st day, then on 2nd day there will be \( 2 x \) lotuses, 3rd day there will be \( (2 \times 2 x=4 x) \) lotuses and so on. If there are 255 lotuses on 5th day, find the total number of lotuses on 7th day.
The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs 300. Represent the situation algebraically and geometrically.
Maximise the number of toys that can be purchased with amount K in C++
A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively $1094,\ 1812,\ 2050$ and $2751$. Find the total number of tickets sold on all the four days.
The weather department has predicted that a thunderstorm is likely to occur on a certain day. Suppose you have to go out on that day. Would you carry an umbrella? Explain.
Get the week number in MySQL for day of week?
Find number of times every day occurs in a Year in Python
Get Day Number of Week in Java
Get the day of week for a particular date in Java
Java Program to get day of week for the last day of each month in 2019
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
Kickstart Your Career
Get certified by completing the course

Get Started