# Thread: Applications Using Equations with Fractions

1. ## Applications Using Equations with Fractions

So this sounds easy but I just dont even know where to start.

What number can be added tom both the numerator and denominator of 16/37 to produce 5/8?Let x be the number in question. What fraction is produced when x is added to both the numerator and the denominator of 16/37.

2. If we let $\displaystyle x$ be the number that we add to both the numerator and the denominator, i.e. $\displaystyle \frac{16 + x}{37 + x}$, this should be produce $\displaystyle \frac{5}{8}$.

In other words, we force the two fractions to be equal and whatever value we get for $\displaystyle x$ after solving the equation must be the number.

So we want to solve: $\displaystyle \frac{16 + x}{37 + x} = \frac{5}{8}$

Start off by cross multiplying to get: $\displaystyle 128 + 8x = 185 + 5x$

Can you continue on?

3. ohh ok. but if your cross multiplying, isnt 5x37=185?
ok so then solving the answer would be 19 right?

4. Whoops, it was a typo. I was merely .. uh.. testing you

To see if you're correct, plug in $\displaystyle x = 19$ to your original equation. Does your fraction reduce to $\displaystyle \frac{5}{8}$ ?

5. yes!thank you