It has been discovered in a certain state that the relationship between the number of snow shovels demanded varies linearly with its price.
When the price per item was $ 38 ,2200 items were demanded;
When the price was $ 49 , 2125 items were demanded.
Determine the price per item when 2143 snow shovels are demanded. $
Above what price will the demand be zero ? $
snowshovels=k*price + constant
2200=k*38 +constant
2125=k*49 +constant
subtract second from first
75=-k*9 k=-75/9
Now find the constant
2200=(-75/9)38 + constant
constant=2200+316.68
2143=(-75/9)P+2516.68
solve for price
thank you
To determine the price per item when 2143 snow shovels are demanded, we can use the concept of linear relationships. In a linear relationship, we can use two points to find the equation of the line, and then use that equation to solve for any unknown value.
Let's use the given information to find the equation of the line for the relationship between the number of snow shovels demanded and the price.
First, we need to find the slope of the line. The slope represents the rate at which the number of snow shovels demanded changes with respect to the price.
The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Using the given points (38, 2200) and (49, 2125), we can calculate the slope as:
m = (2125 - 2200) / (49 - 38) = -75 / 11 ≈ -6.82
Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation for this relationship. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (38, 2200) and the slope -6.82, we can write the equation as:
y - 2200 = -6.82(x - 38)
Simplifying the equation, we get:
y = -6.82x + 2595.16
Now, we can substitute the value of y (2143, as given in the question) into the equation to find the corresponding price per item:
2143 = -6.82x + 2595.16
Rearranging the equation to solve for x:
-6.82x = 2143 - 2595.16
-6.82x = -452.16
x ≈ 66.39
Therefore, the price per item when 2143 snow shovels are demanded is approximately $66.39.
To find the price at which the demand will be zero, we need to find the x-intercept of the line. This represents the price per item when the demand is zero.
For the demand to be zero, y (the number of snow shovels demanded) will be equal to 0. Therefore, we can substitute y = 0 in the equation and solve for x:
0 = -6.82x + 2595.16
-6.82x = -2595.16
x ≈ 380.29
Therefore, the demand will be zero when the price per item is above approximately $380.29.