Find the Fraction Brainteaser (Suitable for Beginning Algebra)

[Otis]

The denominator of a fraction is greater than its numerator by 22, but, if 4 were added to the numerator, then the value of the fraction would become 3/5.

What is the fraction?

?

[imath]\;[/imath]

 

[lookagain]

Spoiler

Let \(\displaystyle \ \dfrac{x}{x + 22} \ \ \) be the original fraction.

Then \(\displaystyle \ \dfrac{x + 4}{x + 22} \ \ \) is the new fraction.

So, \(\displaystyle \ \dfrac{x + 4}{x + 22} \ = \ \dfrac{3}{5}. \)

\(\displaystyle 5(x + 4) \ = \ 3(x + 22) \)

\(\displaystyle 5x + 20 \ = \ 3x + 66 \)

\(\displaystyle 2x = 46 \)

\(\displaystyle x = 23\)

The original fraction is \(\displaystyle \ \dfrac{23}{45}.\)

 

[Deleted member 4993]

The denominator of a fraction is greater than its numerator by 22, but, if 4 were added to the numerator, then the value of the fraction would become 3/5.

What is the fraction?

?

[imath]\;[/imath]

I sent this problem to my grandson. Let's see what he does with it.

 

[Dr.Peterson]

The denominator of a fraction is greater than its numerator by 22, but, if 4 were added to the numerator, then the value of the fraction would become 3/5.

What is the fraction?

?

[imath]\;[/imath]

Without algebra, we can do it this way:

Spoiler

Adding 4 to the numerator reduces the difference to 18. Since the numerator is now 3 of 5 parts, so that the difference is 2 parts, we know that one part is 9, and the new fraction is 9/9*3/5 = 27/45. The original fraction is 23/45.

 

[Otis]

Since the numerator is now 3 of 5 parts…

Wish I'd thought of that!

[imath]\;[/imath]