Please help me with this word problem

Question

If a number is added to the numerator of 9/54 and twice the number is added to the denominator of 9/54, the resulting fraction is equivalent to 1/5. The unknown number is what?

Answer 1

We are adding a number... let's call that number: n

 

We are adding n to the numerator and 2n to the denominator of 9/54... so we have:

 

  9+n  

54+2n

 

we know that this new fraction is equivalent to 1/5... so we can write:

 

  9+n   =  1  
54+2n      5

 

We now need to solve this equation for n... since we have a denominator, you should cross-multiply everything... and you get:

 

(9+n)5 =1(54+2n)

 

Distribute the 5 and the 1...

 

45 + 5n = 54 + 2n

 

collect the "n" terms on one side and move everything else to the other side

 

45 + 5n = 54 + 2n

 

5n – 2n = 54 - 45 <== combine like terms

 

3n = 9 <== divide both sides by 3 to isolate n

 

n = 3 <== TADA! you have your answer.

Answer 2

(9 + n)/(54 + 2n) = 1/5

 

If we cross-multiply, we get:

5(9 + n) = 1(54 + 2n)

45 + 5n = 54 + 2n

3n + 45 = 54

3n = 9

n = 3

 

Let's check our answer:

(9 + 3) / (54 + 6) = 1/5

12 / 60 = 1/5

(4*3) / (4*15) = 1/5

3/15 = 1/5

3/(3*5) = 1/5

1/5 = 1/5