Question

Rob owns stock in Dowc Beverage Co. and Agram Imports. He owns 86 more shares of Agram Imports, which pays a dividend of $5.15 per share, than he does of Dowc Beverage Co., which pays $6.52 per share. If Rob receives $4,585.15 in dividends annually, how many shares of Agram Imports does he own?

Answer 1

Number of shares owned by Rob in Agram Imports = 441

Step-by-step explanation:

Let,

the number of shares owned in Agram = A

and

the number of shares owned in Dowc Beverage Co. = D

Where he owns 86 more shares of Agram Imports than he does of Dowc Beverage Co. then,

A = D + 86

when D is made the subject of the equation,

D = A - 86

Also, if Dowc Beverage Co. pays a dividend of $6.52 per share

Total payment from Dowc = $6.52D

Where Agram Imports pays a dividend of $5.15 per share,

Total payment from Agram Imports = $5.15A

Therefore, total payments received by Rob from both companies

= 6.52D + 5.15A

If Rob receives $4,585.15 in dividends annually then,

6.52D + 5.15A = 4,585.15

Recall that D = A - 86

substituting into the equation above'

6.52(A - 86) + 5.15 = 4585.15

6.52A - 560.72 + 5.15A = 4585.15

6.52A + 5.15A -560.72 = 4585.15

11.67A - 560.72 = 4585.15

Collecting like terms

11.67A = 4585.15 + 560.72

11.67A = 5145.87

Divide both sides by 11.67

`(11.67A)/(11.67) = (5145.87)/(11.67)\\A = 440.9486\\A`

A ≈ 441 Shares

As such, Number of shares owned by Rob in Agram Imports is 441

Answer 2

Let us assume the number of
shares that Rob has of Dowc Beverages Co. = x
Then
Number of shares of Agram imports held by Rob = x + 86
So
The equation can be written as
6.52x + 5.15(x + 86) = 4585.15
6.52x + 5.15x + 442.90 = 4585.15
11.67x = 4585.15 - 442.90
11.67x = 4142.25
x = 4142.25/11.67
= 354.95
= 355
Then
Number of Agram imports shares that Rob owns = x + 86
= 355 + 86
= 441