Let's first establish what we already know for this problem.
x = total number of hotdogs sold
y = total profit from total sales of hotdogs
Let's also establish the other equations which we will require in order to solve this problem.
Equation No. 1 -
Profit for 40 hotdogs = $90 profit
Equation No. 2 -
Profit for 80 hotdogs = $210 profit
STEP-BY-STEP SOLUTION
From this, we can use the formula y = mx + b & substitute the values for x & y from one of the two previous equations into the formula in order to obtain the values of m & b for the final equation. Here is an example of the working out as displayed below:
Firstly, using the first or second equation, we make either m or b the subject. Here I have used the first equation and made m the subject:
Equation No. 1 -
y = mx + b
90 = m ( 40 ) + b
40m = 90 - b
m = ( 90 - b ) / 40
Now, make b the subject in the second equation as displayed below:
Equation No. 2 -
y = mx + b
210 = m ( 80 ) + b
210 = 80m + b
b = 210 - 80m
Then, substitute m from the first equation into the second equation.
Equation No. 2 -
b = 210 - 80m
b = 210 - 80 [ ( 90 - b ) / 40 ]
b = 210 - [ 80 ( 90 - b ) / 40 ]
b = 210 - 2 ( 90 - b )
b = 210 - 180 - 2b
b - 2b = 30
- b = 30
b = - 30
Now, substitute b from the second equation into the first equation.
Equation No. 1 -
m = ( 90 - b ) / 40
m = ( 90 - ( - 30 ) / 40
m = ( 90 + 30 ) / 40
m = 120 / 40
m = 3
Through this, we have established that:
m = 3
b = - 30
Therefore, the final equation to model the final profit, y, based on the number of hotdogs sold, x, is as follows:
y = mx + b
y = ( 3 )x + ( - 30 )
ANSWER:
y = 3x - 30
The number of quarts of orange juice did Rebecca use is 7
Given that 28 glasses with orange juice are filled for a camp breakfast
Each glass holds 1 cup of juice
We need to find the number of quarts of orange juice did Rebecca use
We know that a quarts has 4 cups
We need to calculate the quarts from 28 glasses
Let the number of the quarts be x
So the equation formed is
4x = 28
Where x is number of quarts and 28 are the number of glasses
x = 7
Hence the number of quarts is 7
Learn more about Logical reasoning here
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Answer:
gradient=change in y/change in x
=y2-y1/x2-x1
=-8-(-16)/-10-(-8)
=8/-2
=-4
