When building a house, the number of days required to build varies inversely with with the number of workers. One house was built in 19 days by 35 workers. How many days would it take to build a similar house with 5 workers?

The total number of days requires to build a similar house with 5 workers is 133 and this can be determined by forming the linear equation.

Given :

The following steps can be used in order to determine the total number of days to build a similar house with 5 workers:

Step 1 - According to the given data, the number of days required to build varies inversely with the number of workers.

Step 2 - Now, let the total number of workers be 'x' and the total number of days be 'y'. Then the mathematical expression that represents the above situation is:

yx = k

where k is the proportionality constant.

Step 3 - Now, substitute the value of y = 19 and x = 35 in the above equation.

19 35 = k

k = 665

Step 4 - So, the total number of days requires to build a similar house with 5 workers is:

5y = 665

y = 133 days

Therefore, the total number of days requires to build a similar house with 5 workers is 133.

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Let d represent number of days and n represent number of workers.

We have been given that when building a house, the number of days required to build varies inversely with with the number of workers.

We know that the equation represents the relation where y is inversely proportional to x and k is the constant of proportionality.  

So our required equation would be

Upon substituting our given values, we will get:

Since constant of proportionality is 665, so our equation would be .

To find the number of days it will take to build a similar house with 5 workers, we will substitute in our equation as:

Therefore, it will take 133 days for 5 workers to build a similar house.

step-by-step explanation:

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answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204