The numerator of a rational number is 3 less than five times its denominator. When 2 is subtracted from its numerator, and 7 is added to its denominator, the simplest form of the rational number obtained is 5/3. Find the original rational number.
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Answer:
The actual rational number is [tex]\frac{22}{5}[/tex].
Step-by-step explanation:
Here we have been given two rational numbers and the condition is such that the numerator is 3 times less than 5 times its denominator.
Let the denominator of the given rational number be a.
So according to the question numerator is equal to 5a-3
The rational number is now= [tex]\frac{5a-3}{a}[/tex]
Now, again according to the question
⇒[tex]\frac{5a-3-2}{a+7}[/tex] =[tex]\frac{5}{3}[/tex]
⇒[tex]\frac{5a-5}{a+7}[/tex] =[tex]\frac{5}{3}[/tex]
⇒15a-15=5a+35
⇒15a-5a=35+15
⇒10a=50
⇒a=5
∴ numerator= 5a-3
= 25-3
= 22
The actual rational number is [tex]\frac{22}{5}[/tex].