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 times scientific books were sold compared to mystery books is 1000 times or one thousand times.
<h3>How many copies of each book were sold?</h3>
The numbers provided to represent the number of copies that were sold from each book are given in scientific notation. In this type of notation, the exponent represents the number of zeros. Based on this principle, the number of books sold from each type is:
- Science fiction book: 10^6 = 1.000,000 (one million copies)
- Mystery book: 10^3 = 1.000 (one thousand copies)
<h3>How many science fiction book copies were sold in comparison to mystery book copies?</h3>
To find out this, simply divide the number of science fiction book copies into the number of mystery book copies:
- 1,000,000 / 1,000 = 1,000 (one thousand)
Learn more about scientific notation in: brainly.com/question/18073768
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Let's say the original radius was "r", so the circumference is 2πr and the area is πr².
Now when you double the radius, the you get a new circle with radius 2r, circumference 2π(2r) = 4πr, and area π(2r)² = 4πr².
solve for x.
4x−5=7+4y
Add 5 to both sides.
4x−5+5=4y+7+5
4x=4y+12
Divide both sides by 4.
4x/4=4y+12/4
x=y+3
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Have a nice day! :)