# If a large factory sells its new gadgets for $5 each it can sell 1050 per month and if it sells the same gadgets for $9 it will sell 900 per month. Assuming the relationship between price and sales is linear predict the monthly sales of gadgets to the nearest whole number if the price is $12.

## you are given 2 ordered pairs

(5 , 1050) and (9,900)

slope = (900 - 1050)/(9-5) = - 150/4 = - 75/2

N = (-75/2)C + b

using (5,1050)

1050 = (-75/2)(5) + b

1050 + 375/2 = b

b = 2475/2

N = (-75/2)C + 2475/2 or N = -37.5C + 1237.5

where N is the number sold and C is the price of each

so when C = 12

N = -37.5(12) + 1237.5 = 787.5

number sold = 788

## Well, let me put on my "clown" hat and try to predict the monthly sales of gadgets for $12.

Based on the given information, we know that the factory sells 1050 gadgets when the price is $5 and 900 gadgets when the price is $9. So, let's do some math!

First, let's calculate the "price difference" between $5 and $9. It's $9 - $5 = $4.

Now, let's calculate the "sales difference" between 1050 gadgets and 900 gadgets. It's 1050 - 900 = 150 gadgets.

So, we have a price difference of $4 and a sales difference of 150 gadgets.

Since we assume a linear relationship, we can calculate the "sales per price" by dividing the sales difference by the price difference.

150 gadgets ÷ $4 = 37.5 gadgets per dollar.

Now, let's use this information to predict the monthly sales when the price is $12.

$12 × 37.5 gadgets per dollar = 450 gadgets.

Voila! According to my calculations, the monthly sales of gadgets, when the price is $12, should be around 450 gadgets.

Please note that these predictions are based on a linear relationship assumption and market conditions can always vary. Now, wasn't that a "clownishly" funny way to calculate, predict, and answer a question?

## To predict the monthly sales of gadgets when the price is $12, we can use the linear relationship between price and sales.

First, let's find the slope of the line. The slope (m) can be found using the formula:

m = (change in sales) / (change in price)

Using the given information, the change in sales is 1050 - 900 = 150, and the change in price is $5 - $9 = -$4.

So, the slope is:

m = 150 / (-$4) = -37.5

Next, we can use the slope-intercept form of a linear equation:

y = mx + b

where y represents the sales, x represents the price, m is the slope, and b is the y-intercept.

To find the y-intercept (b), we can use one of the given data points. Let's use the data point ($5, 1050):

1050 = -37.5 * 5 + b

1050 = -187.5 + b

b = 1050 + 187.5 = 1237.5

Now we have the equation:

y = -37.5x + 1237.5

To predict the monthly sales when the price is $12, substitute x = 12 into the equation:

y = -37.5 * 12 + 1237.5

y = -450 + 1237.5

y = 787.5

Rounding to the nearest whole number, the predicted monthly sales of gadgets when the price is $12 is approximately 788 units.

## To predict the monthly sales of gadgets at a price of $12, we can use the concept of linear regression. Linear regression is a statistical technique to model the relationship between two variables, in this case, price and sales.

First, let's define the relationship between price and sales using the data given. We have two data points: at $5, the factory sells 1050 gadgets, and at $9, it sells 900 gadgets.

Using this information, we can determine the slope and intercept of the linear relationship. The formula for a linear equation is y = mx + b, where y is the dependent variable (sales), x is the independent variable (price), m is the slope, and b is the intercept.

To find the slope, we use the formula:

m = (y2 - y1) / (x2 - x1)

Let's plug in the values we have:

m = (900 - 1050) / ($9 - $5)

m = -150 / 4

m = -37.5

Next, we can find the intercept (b) by substituting the values of one data point into the equation:

1050 = (-37.5 * $5) + b

1050 = -187.5 + b

1050 + 187.5 = b

b ≈ 1237.5

Now we have the equation for the relationship between price (x) and sales (y):

y = -37.5x + 1237.5

To predict the monthly sales when the price is $12, we substitute x = $12 into the equation:

y = -37.5 * $12 + 1237.5

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