word problems

Question

the numerator of a certain fraction is five times the denominator. if 12 is added to both the numerator and the denominator,the resulting fraction is equivalent to 2.What was the original fraction?

Answer 1

Hi Yesenia,

 

Let's begin by assigning variables for our unknowns:

N = numerator of original fraction

D = denominator of original fraction

 

Now let's form equations from our given information, which will allow us to solve for our unknowns:

 

The first piece of information we are given is that the numerator (N) is 5 times more than the denominator (D), which can be expressed by this equation:

 

N = 5D

 

The other piece of information we are given is that if 12 is added to both the numerator (N) and also to the denominator (D) - it will give the new fraction a value of 2. This information can can be expressed by this equation:

 

(N + 12) / (D + 12) = 2

 

So now we have two equations, which we can use to solve for our 2 unknowns.

 

Let's start by replacing N in the second equation by its equivalent value (5D) from the first equation, giving us this equation:

 

(5D + 12) / (D + 12) = 2

 

Now we can multiply both sides of this equation by the denominator (D + 12) to get rid of the fraction on the left side, which gives us this nice equation allowing us to solve for D:

 

5D + 12 = 2D + 24

 

Getting of the (+ 12) on the left side by subtracting 12 from both sides, gives us:

 

5D = 2D + 12

 

Getting rid of the 2D on the right side by subtracting 2D from both sides, gives us:

 

3D = 12

 

Dividing both sides by 3 gives us our value for D:

 

D = 4

 

Now we can substitute our value for D (4) into our first original equation (N = 5D) to solve for N:

 

N = 5(4) and so after simple multiplication, we now have our value for N:

 

N = 20

 

And so our original fraction (N/D) is 20/4 (answer)

 

We can check our answer by substituting our values for N and D in our second original equation to see if it is a true statement:

 

(N + 12) / (D + 12) = 2

 

(20 + 12) / (4 + 12) = 2 ( after substitution)

32 / 16 = 2 (after simplification)

2 = 2 (after division)

 

All checks out and so we are confident that our solution is correct.

 

Thanks for sharing this problem and I'm available online should you need more assistance.

 

God bless, Jordan.

Answer 2

Original fraction 5d/d. Adjusted fraction  (5d+12)/(d+12)=2

5d+12=2d+24,  3d=12, d=4

20/4 original fraction, 32/16 when 12 added to both numerator and denominator