A number is thrice another number. The sum of their reciprocals is 4. Find The numbers.

Question

Aa_yangaTyro

Asked: March 30, 20212021-03-30T03:37:04+00:00 2021-03-30T03:37:04+00:00In: High School/Senior Secondary School

Solve the following by using rational algebraic expressions.

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Pocholo · Answer 1 · 2021-03-30T05:32:17+00:00

Pocholo Tyro

This answer was edited.

a number = x

thrice another number = 3x

the sum of their reciprocal is equal to 4

1/x + 1/3x = 4

LCD = 3x

3x (1/x + 1/3x = 4)

3x/x + 3x/3x = 3x(4)

3 + 1 = 12x

4 = 12x

4/12 = x

1/3 = x

acedstud · Answer 2 · 2021-03-30T06:52:06+00:00

acedstud

This answer was edited.

Let the first number be $x$ , then the other number is $3x$ and their reciprocals are $\dfrac{1}{x}$ and $\dfrac{1}{3x}$ .

Thus, $\dfrac{1}{x}+\dfrac{1}{3x}=4$ .

Multiplying through by the Least Common Denominator (LCD), which is $3x$ , we have $3x\left(\dfrac{1}{x}+\dfrac{1}{3x}\right)=3x(4)$

$\Rightarrow\dfrac{3x}{x}+\dfrac{3x}{3x}=12x$

$\Rightarrow3+1=12x\Rightarrow4=12x\Rightarrow x=\dfrac{4}{12}=\dfrac{1}{3}$

Thus, the first number is $x=\dfrac{1}{3}$ and the other number is $3x=3\times\dfrac{1}{3}=1$ .

Therefore, the numbers are $\dfrac{1}{3}$ and 1.