HOW DO YOU SET THIS QUESTION OUT ALGEBRAICALLY?!! PLEASE HELP ME!!!

anne is five years older than her sister Peter, but 7 years younger than her brother Mike. If the sum of their ages is 86, then how old is mike.. Iknow mike is 35 but that was through trial and error, i want to know how to do it in algebraic format. THANKS GUYS!!!

A = P + 5
A = M - 7
A + P + M = 86
P+5=M-7
P = M -12
A = M - 7
M - 7 + M -12 + M = 86
3M = 105
M = 35
A = 28
P = 23

let peter's age be x
and let mike's age be y.

then,anne's age = x + 5

now, x + 5 = y - 7 => x - y = -12

also, x + (x + 5) + y = 86 => 2x + y = 81

solving the above two equations,we get

x = 23 and y = 35

therefore,mike's age is 35 years

When answering these type of questions, write a formula for each statement.

A=P+5
A=M-7
A+P+M=86

3 equations, 3 unknowns.

Rearrange to
P=A-5
M=A+7

Substitue into 3rd equation

A+(A-5)+(A+7)=86

You can solve from here.

assume peter's age x
then anne's age=x+5 ........... she is 5 years older
Mik'es age is x+5+7................ he is 7 years older than anne
sum of their ages=x+x+5+x+5+7=3x+17=86
3x=69
x=23

hence mikes age is 23+5+7=35 years

Mike = x years
Anne = x-7
Peter = x-12
solve for x in
x+(x-7)+(x-12) = 86