Question

The numerator of a rational number is less that it’s denominator by 7.If the new number becomes 3/2 when the numerator is tripled and the denominator is increased by 16, find the original number
Pls help me with this question

Answer 1

Answer:

$\frac{23}{30}$

Step-by-step explanation:

let the denominator of the original fraction be x, then

$\frac{x-7}{x}$ ← is the original fraction

After the given changes, that is

$\frac{3(x-7)}{x+16}$ = $\frac{3}{2}$ ( cross- multiply )

6(x - 7) = 3(x + 16) ← distribute parenthesis on both sides

6x - 42 = 3x + 48 ( subtract 3x from both sides )

3x - 42 = 48 ( add 42 to both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Thus

$\frac{30-7}{30}$ = $\frac{23}{30}$ ← the original rational number