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

See Explanation

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.

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

Step 3: Solve for x

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

Factorize

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

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

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

`(4)/(3x) = 4`

Cross multiply

`4 = 3x * 4`

`4 = 12x`

Solve for x

`x = (4)/(12)`

`x = (1)/(3)`

Step 4; Verify

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

Substitute
`x = (1)/(3)`

`(1)/(1/3) + (1)/(3*1/3) = 4`

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

`3 + 1 = 4`