Question

A positive integer is twice another. The sum of the reciprocals of the two positive integers is 3/10 find the integers

Answer 1

x = 2y

1/x + 1/y = 3/10

Since we have a value for x, let's plug it into the second equation.

1/2y + 1/y = 3/10

Now, let's make the denominators equal.

Multiply the second term by 2.

1/2y + 2/2y = 3/10

Multiply the final term by 0.2y

1/2y + 2/2y = 0.6y/2y

Compare numerators after adding.

3 = 0.6y

Divide both sides by 0.6

y = 5

Now that we have the value of the second integer, we can find the first.

x = 2y

x = 2(5)

x = 10

Let's plug in these values in our equations to verify.

10 = 2(5) √ this is true

1/10 + 1/5 = 3/10 √ this is true

The first integer is equal to 10, and the second is equal to 5.