
Find given that and .
Answer
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Hint: Here and are given. We can find the combined ratio using the common variable . For that we have to make the number corresponding to the same in both the ratios. Multiplying both numbers in a ratio by an integer will not change the ratio.
Useful formula:
A ratio does not change if we multiply both the numbers by the same integer.
That is, , for any .
Complete step-by-step answer:
We are given that and .
We have to find .
Here we can see is common in both the ratios.
So we can find the ratio using it.
We know that a ratio does not change if we multiply both the numbers by the same integer.
So we can multiply the given ratios so that the number corresponding to will be the same in both the ratios.
Now the numbers corresponding to are and .
We can see their least common multiple is 105, where
Consider .
Multiplying both numbers by we get, .
This gives,
Consider .
Multiplying both numbers by we get, .
This gives,
Now we have, and .
Combining these two we get,
Note: Here, to make the numbers corresponding to the same, we multiply both the ratios by and respectively. Likewise we can divide the terms in a ratio without changing the ratio. That is, , by cancelling the common factor . But in this case, by dividing we cannot make the terms in the ratio the same.
Useful formula:
A ratio does not change if we multiply both the numbers by the same integer.
That is,
Complete step-by-step answer:
We are given that
We have to find
Here we can see
So we can find the ratio using it.
We know that a ratio does not change if we multiply both the numbers by the same integer.
So we can multiply the given ratios so that the number corresponding to
Now the numbers corresponding to
We can see their least common multiple is 105, where
Consider
Multiplying both numbers by
This gives,
Consider
Multiplying both numbers by
This gives,
Now we have,
Combining these two we get,
Note: Here, to make the numbers corresponding to
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