It has been found that the supply of lamps varies linearly with its price.
When the price per item was $ 94.67 ,64 items are supplied;
When the price was $ 134.67 , 124 items are supplied.
How many lamps are supplied when the price per item is $ 118.00 ?
What is the lowest price above which lamps will be supplied ? $
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To find the number of lamps supplied when the price per item is $118.00, we can use the relationship between the price and the number of items supplied, which is stated to vary linearly.
First, let's define the variables:
Let x be the price per item (in dollars),
Let y be the number of items supplied.
We know that when the price per item is $94.67, 64 items are supplied, and when the price per item is $134.67, 124 items are supplied.
Using this information, we can form two points on the linear relationship:
Point 1: (x1, y1) = ($94.67, 64)
Point 2: (x2, y2) = ($134.67, 124)
Next, let's find the slope of the line (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the values:
m = (124 - 64) / ($134.67 - $94.67)
Simplifying, we get:
m = 60 / $40
Calculating the slope, we find:
m = 1.5
Now that we have the slope, we can find the equation of the line using the point-slope formula:
y - y1 = m(x - x1)
Using Point 1:
y - 64 = 1.5(x - $94.67)
Simplifying, we get:
y = 1.5x - $130.01
Now, we can substitute the given price of $118.00 into the equation and solve for the number of lamps supplied (y):
118 = 1.5x - $130.01
Rearranging the equation, we get:
1.5x = 118 + $130.01
1.5x = $248.01
Dividing both sides by 1.5, we find:
x = $164.67
Therefore, when the price per item is $118.00, the number of lamps supplied is 164.
To find the lowest price above which lamps will be supplied, we need to determine the x-intercept of the line (where the number of lamps supplied is 0).
Setting y = 0 in the equation:
0 = 1.5x - $130.01
Solving for x, we find:
1.5x = $130.01
x = $86.67
Therefore, the lowest price above which lamps will be supplied is $86.67.