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2 years ago

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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 triple

d and the denominator is increased by 16, find the original number
Pls help me with this question

1 answer:

Murljashka [212]2 years ago

3 0

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

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2 years ago

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2 years ago

Read 2 more answers

HELP!! I NEED THIS QUICKLY

Elza [17]

Answer:

A and D

Step-by-step explanation:

We are given that

(3/4,2/3),(1/4,1),(1,1/2) and (1/2,1)

$x_1=\frac{3}{4}$

$y_1=\frac{2}{3}$

$x_2=\frac{1}{4},y_2=1$

$x_3=1,y_3=\frac{1}{2}$

$x_4=\frac{1}{2},y_4=1$

k= $\frac{1}{2}$

Direct proportion:

$\frac{x}{y}=k$

Inverse proportion: $xy=k$

$\frac{x_1}{y_1}=\frac{3}{4}\times \frac{3}{2}=\frac{9}{8}\neq \frac{1}{2}$

Therefore, it is not in direct proportion.

$\frac{1}{4\times 2}=\frac{1}{8}\neq\frac{1}{2}$

$\frac{1}{\frac{1}{2}}=2\neq \frac{1}{2}$

$x_1y_1=\frac{3}{4}\times \frac{2}{3}=\frac{1}{2}$

$x_2y_2=\frac{1}{4}\times 2=\frac{1}{2}$

$x_3y_3=1\times \frac{1}{2}=\frac{1}{2}$

$x_4y_4=\frac{1}{2}\times 1=\frac{1}{2}$

Therefore, $xy=k=\frac{1}{2}$

Hence, the given points form an inverse variation .

$xy=\frac{1}{2}$

$y=\frac{1}{2x}$

Option A and D is true.

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2 years ago