Answer:
15 muffins are cinnamon.
Step-by-step explanation:
Given that:
Number of muffins baked = 50 muffins
Chocolate chip muffins = 1/5 of 50 =
Chocolate chip muffins = 10 muffins
Blueberry muffins = 1/2 of 50 =
Blueberry muffins = 25
Cinnamon muffins = Muffins baked - chocolate chip muffins - blueberry muffins
Cinnamon muffins = 50 - 10 - 25
Cinnamon muffins = 50 - 35 = 15
Hence,
15 muffins are cinnamon.
Use the polynomial remainder theorem. It says that a polynomial has remainder
upon division by
.
Here we have
and , so the remainder is
Our goal here is to somehow "surgically remove" the repeating part of the number, so let's start by putting the original value in a variable and messing around with it a bit.
We'll let . We want to cut the
bit off completely, so let's create the scalpel that'll let us do that. If
, then we can also say that
. Maybe I was lying a bit: the
is our real scalpel here, and
is where we'll be making the cut. Mathematically, a "cut" is almost always shorthand for subtraction, so let's see what our operation (cutting
off of
) leaves us with:
The operation was a success! We can now simply divide either side by 9 to find , which, when reduced by dividing the numerator and denominator by 3, gives us