Question

a fraction equals 8/9. the numerator is 2 more than6 times the quotient of the denominator and 7. find the reciprocal of the original fraction

Answer 1

Let's start by assigning variables to the unknowns in the problem. Let x be the numerator and y be the denominator of the original fraction. We know that:

x/y = 8/9

Now let's translate the second sentence of the problem into an equation:

x = 6(y/7) + 2

We can simplify this equation by multiplying both sides by 7:

7x = 6y + 14

Now we have two equations with two unknowns. We can solve for x in the first equation and substitute it into the second equation:

x = (8/9)y

7(8/9)y = 6y + 14

Multiplying both sides by 9/8:

7y = 81/4

Dividing both sides by 7:

y = 81/28

Now we can substitute y back into the first equation to solve for x:

x = (8/9)(81/28) = 27/7

So the original fraction is 27/81, which simplifies to 1/3. The reciprocal of 1/3 is 3/1 or simply 3.