Question

Problem # 1: Number problemOne number is three times another. The sum of their reciprocals is 4. What are the two numbers? Step 1: Represent the unknownLet x = the number and 3x = other number_____ =reciprocal of the number, _____ = reciprocal of the other number Step 2: Decide what mathematical operations should be used.1 + 13 =________ Step 3: Apply the mathematical operations to be used3x ( 1+ 13= 4 )3x3x( 1) + 3 ( 13) = 3(4)____________ = 12x4 = 12xx = _______, this is the number Step 4: Verify your answer (2points) Fill in the blank in step 1 to 3, and for Step 4, show the complete solution *

Answer 1

Answer:

See Explanation

Step-by-step explanation:

Required

Complete the blanks

Step 1: The unknowns

$x = the\ number$

$3x = the\ other\ number$

Step 2: Sum of Reciprocals

The implies that both numbers be inversed, then added together.

i.e.

$\frac{1}{x} + \frac{1}{3x} = 4$

Step 3: Solve for x

$\frac{1}{x} + \frac{1}{3x} = 4$

Factorize

$\frac{1}{x}(1 + \frac{1}{3}) = 4$

$\frac{1}{x}(\frac{3 + 1}{3}) = 4$

$\frac{1}{x}(\frac{4}{3}) = 4$

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

Cross multiply

$4 = 3x * 4$

$4 = 12x$

Solve for x

$x = \frac{4}{12}$

$x = \frac{1}{3}$

Step 4; Verify

$\frac{1}{x} + \frac{1}{3x} = 4$

Substitute $x = \frac{1}{3}$

$\frac{1}{1/3} + \frac{1}{3*1/3} = 4$

$3 + \frac{1}{1} = 4$

$3 + 1 = 4$