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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

Respuesta :

Answer:

[tex]\frac{23}{30}[/tex]

Step-by-step explanation:

let the denominator of the original fraction be x, then

[tex]\frac{x-7}{x}[/tex] ← is the original fraction

After the given changes, that is

[tex]\frac{3(x-7)}{x+16}[/tex] = [tex]\frac{3}{2}[/tex] ( 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

[tex]\frac{30-7}{30}[/tex] = [tex]\frac{23}{30}[/tex] ← the original rational number

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