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telo118 [61]
3 years ago
10

It takes 1 1/2 cups of flour, 1 1/4 cups of sugar, and 1/2 cup of butter to bake fifteen shortbread cookies. If Ramon has 5 cups

of flour, 4 cups of sugar, and 1 3/4 cups of butter, how many shortbread cookies can he bake?
PLZ PLZ PLZ PLZ PLZ HELP I NEED A DETAILED EXPLINATION PLZ!
Mathematics
1 answer:
Stolb23 [73]3 years ago
7 0
Short answer 48 cookies
Remark

This is an extremely valuable question if you are going to take chemistry at some point. You have to calculate all three to see what the limiting ingredient is.

Flour
Assuming that all of the flour will be used, you set up a proportion to find out how many cookies will be produced.

1.5 cups of flour / 15 cookies = 5 cups of flour / x     Cross multiply
1.5 x  = 15 * 5
1.5 x = 75                       Divide by 1.5
x = 75/1.5
x = 50                             cookies are possible

Sugar
Now you must do the same thing with the sugar
1.25 pounds sugar/15 cookies = 4 / x      Cross multiply
1.25 x = 4 * 15
1.25 x = 60                         Divide both sides by 1.25
x = 60/1.25                     
x = 48               cookies possible with 4 pounds of sugar.

Butter
0.5 pounds of butter/15 cookies = 1.75 pounds of butter /x   Cross Multiply
0.5 * x = 15 * 1.75
0.5 * x = 26.25       Divide by 0.5
x = 26.25 / 0.5
x = 52.5                  Cookies.

Conclusion
The limiting ingredient is the sugar. You can only make 48 cookies with that amount of sugar. 

So you will have left over flower. You will have left over butter (even if you round down). But you will use all your sugar. It is the least amount.
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Carlota wrote the equation y + 1 = 2 (x - 3) for the line passing through the points (-1, 3) and (2, 9). Explain and correct her
Art [367]

For this case we have the following equation:


y + 1 = 2 (x - 3)

That can be rewritten in the form y = mx + b

Where:


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So, we have:


y + 1 = 2 (x - 3)\\y + 1 = 2x-6\\y = 2x-6-1\\y = 2x-7

Where:


m = 2 is the slope


b = -7 is the cut point


Carlota has the following points:


(-1, 3) and (2, 9)


To know if the line y = 2x-7 passes through these points, we must replace them in the equation and the equality must be fulfilled. So:


Point (-1, 3):


Substituting:


3 = 2 (-1) -7\\3 = -2-7

3 = -9 It's false, equality is not met. The point (-1, 3) does not go through the line.


The equation written by Carlota is erroneous, the procedure to follow is:


Given(x1, y1) = (- 1, 3) and(x2, y2) = (2, 9), we find the slope:


m=\frac{(y2-y1)}{(x2-x1)}

m=\frac{(9-3)}{(2-(-1))}

m=\frac{6}{3}

m=2

We observe that the slope found by Carlota is the same. Let's see cut point "b". For this we substitute any of the points given in the equation:


y = 2x + b

Substituting (2,9) we have:


9 = 2 (2) + b\\9 = 4 + b\\b = 9-4\\b = 5

Thus, Carlota's error was at the cut-off point. The correct equation of the line that passes through the given points is y = 2x + 5

Answer:


The correct equation of the line that passes through the given points is y = 2x + 5

Carlota's mistake was at the cutoff point


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Step-by-step explanation:

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