A recipe uses 3 cups of flour and 2 cups of sugar write the ratio as a fraction
2 answers:
Answer:
Step-by-step explanation:
A recipe uses 3 cups of flour and 2 cups of sugar.
The ratio is the relation between two quantities of the same kind.
For example:
There are 10 boys and 9 girls in a class. The ratio of boys to girls is 10 : 9
We can write the ratio in fraction form : and also we can simplify the ratio.
Now let's move to our question.
The ratio of 3 cups of flour and 2 cups of sugar is 3:2
This can be written as
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A good place to start is to set to y. That would mean we are looking for
to be an integer. Clearly,
, because if y were greater the part under the radical would be a negative, making the radical an imaginary number, not an integer. Also note that since
is a radical, it only outputs values from
, which means y is on the closed interval:
.
With that, we don't really have to consider y anymore, since we know the interval that is on.
Now, we don't even have to find the x values. Note that only 11 perfect squares lie on the interval , which means there are at most 11 numbers that x can be which make the radical an integer. All of the perfect squares are easily constructed. We can say that if k is an arbitrary integer between 0 and 11 then:
Which is strictly positive so we know for sure that all 11 numbers on the closed interval will yield a valid x that makes the radical an integer.