Question

When is decreased by the quotient of a rational number and 30
the result
is the rational number itself. Find the number.​

Answer 1

Step-by-step explanation:

When 65/2 is decreased by the quotient of a rational number and 3/10, the result is the rational number itself. What is the number?

Let the rational number be x. The quotient after dividing the number x by 3/10 is x / (3/10), which is 10∗x/3 .

Subtracting this quotient from 65 / 2 is giving back the same rational number, which is x, therefore, we have

65/2−(10∗x)/3 = x, this leads to

195 - 20*x = 6x,

which is nothing but

195 = 26*x and therefore x = 195/26 , which is [math] 15 / 2 [/math].

The quotient of 15 / 2 divided by 3/10 is 25 and when you reduce 65/2 by 15/2, you get 25 and thus the answer 15/2 is verified, which is the required number!