the 7th grade students at Palm Coast Middle School made some apples pies for a bake sale. The school cafeteria also donated 9 pi
es towards the effort. All the pies at the sale were cut into 8 pieces. If at least 224 pieces of pies were sold in all, how many pies did the students bake?
2 answers:
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Answer:
Step-by-step explanation:
By the Intersecting Secants Theorem, we know that:
Having this, we can find the value of "x" by solving for "x":
Applying Distributive property:
Subtract 25 from both sides of the equation:
And finally dviding both sides of the equation by 5, we get:
Remember the divisibility rule for 9. The sum of the digits of the number must be divisible by nine.
Let the digit be
. Then 
has to be divisible by nine. Recalling that 
, we note that 
.
Let the digit be
Answer:
-10
Step-by-step explanation:
You are asked to tell the y-value of the solution. You can find the whole solution and then report the y-value, or you can just find the y part of the solution. We choose the latter.
This is basically done by eliminating the x-variable. It can be done using the "elimination" method of solving these equations. And it can also be done using the "substitution" method of solving these equations. We choose the latter.
Add 14 to the second equation to solve for x:
... x = y + 14
Substitute this into the first equation.
... 3(y +14) -y = 22
... 2y +42 = 22 . . . . . . simplify
... y +21 = 11 . . . . . . . . divide by 2
... y = -10 . . . . . . . . . . subtract 21
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<em>Comment on additional solution methods</em>
A graphing calculator can show you the solution, as in the attachment. Of the solution (x, y) = (4, -10), we are only interested in y = -10.
Cramer's rule can find just one variable value, too. For that, it is convenient to write the system as ...
- 3x -y = 22
- x - y = 14 . . . . . add 14-y to the equation given
Then the solution for y is ...
... y = (22·1 -14·3)/(-1·1 -(-1)·3) = -20/2 = -10
