Taking into account the rule of three, there are 13.90624 caboodles in 8.9 doodles.
The rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
In first place, the following rule of three can be applied: If for every 10 doodles there are 5 noodles, for 8.9 doodles how many noodles are there?
10 doodles ⇒ 5 noodles
8.9 doodles ⇒ x
So: [tex]x=\frac{8.9 doodlesx 5 noodles}{10 doodles}[/tex]
Solving:
x= 4.45 noodles
Now, it is possible to apply a rule of three like the following: If there are 4 noodles for every 1 mole, there are 4.45 noodles for every how many moles?
4 noodles ⇒ 1 mole
4.45 noodles ⇒ x
So: [tex]x=\frac{4.45 noodlesx 1 mole}{4 noodles}[/tex]
Solving:
x= 1.1125 moles
Finally, one last rule of three can be applied: if 2 moles have a mass of 23 caboodles, 1.1125 moles have how much mass?
2 moles ⇒ 23 caboodles
1.1125 moles ⇒ x
So: [tex]x=\frac{1.1125 molesx23 caboodles}{2 moles}[/tex]
Solving:
x= 13.90624 caboodles
Finally, there are 13.90624 caboodles in 8.9 doodles.
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