Problem

A clothing business finds there is a linear relationship between the number of shirts, $n$, it can sell and the price, $p$, it can charge per shirt. In particular, historical data shows that 24000 shirts can be sold at a price of $\$ 76$, while 41000 shirts can be sold at a price of $\$ 25$. Give a linear equation in the form $p=m n+b$ that gives the price $p$ they can charge for $n$ shirts. Answer: $p=$ Round the value of your slope to three decimal places. Be careful to use the proper variable and use the Preview button to check your syntax before you submit your answer.

Solution

Step 1 :We are given two points on the line: (24000, 76) and (41000, 25).

Step 2 :We can use these two points to find the slope of the line, which is given by the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Step 3 :Once we have the slope, we can use the point-slope form of a line, \(y - y_1 = m(x - x_1)\), to find the equation of the line.

Step 4 :We can then rearrange this equation to the slope-intercept form, \(y = mx + b\).

Step 5 :The slope of the line is -0.003 and the y-intercept is 148.0.

Step 6 :Therefore, the equation of the line is \(p = -0.003n + 148\). This equation gives the price \(p\) they can charge for \(n\) shirts.

Step 7 :\(\boxed{p = -0.003n + 148}\)

From Solvely APP
Source: https://solvelyapp.com/problems/25293/

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