Respuesta :
Alright, lets get started.
Suppose Cary's current age = x
Suppose Dan's current age = y
Cary is 9 years older than Dan (given in question), means :
[tex] x = y + 9 [/tex] ...............................equation (1)
After 10 years Cary's age = (x+10)
After 10 years Dan's age = (y+10)
In 10 years the sum of their ages will be 81, means
[tex] (x+10)+(y+10) = 81 [/tex]
[tex] x + y + 20 = 81 [/tex]
Subtrating 20 in both sides
[tex] x + y + 20 - 20 = 81- 20 [/tex]
[tex] x + y = 61 [/tex] .................................... equation (2)
From equation (1), putting the value of x in equation (2)
[tex] y + 9 + y = 61 [/tex]
[tex] 2y + 9 = 61 [/tex]
Subtrating 9 in both sides
[tex] 2 y + 9 - 9= 61 - 9 [/tex]
[tex] 2 y = 52 [/tex]
Dividing by 2 in both sides
[tex] \frac{2y}{2} = \frac{52}{2} [/tex]
[tex] y = 26 [/tex]
[tex] x = y + 9 = 26 + 9 [/tex]
[tex] x = 35 [/tex]
It means Cary's age is 35 and Dan's age is 26. : Answer
Hope it will help :)
