Question 1034417
problem 1:

a = tens digit
b = units digit


number is represented by 10a + b
number formed by reversing the digits is represented by 10b + a.
the sum of the number and the number with the digits reversed is equal to 88.
this means that 10a + b + 10b + a = 88.
combine like terms to get 11a + 11b = 88
you are given that the units digits is 3 times the tens digit.
this means that b = 3a
in the equation of 11a + 11b = 88, replace b with 3a to get:
11a + 11*3a = 88
simplify to get 11a + 33a = 88
combine like terms to get 44a = 88
divide both sides of this equation by 44 to get a = 2
since b = 3a, this means that b = 6
since b is the units digit and a is the tens digit, this means that the number is 26.
the number with the digits reversed is 62.
26 + 62 = 88
the problem is solved.
the number is 26.

problem 2:


x = the man's age today.
the man's age 20 years from now is equal to the man's age 20 years before now.
this means that (x+20) = 3 * (x-20).
simplify to get x + 20 = 3x - 60
subtract x from both sides of this equation and add 60 to both sides of this equation to get 20 + 60 = 3x - x
simplify to get 80 = 2x
divide both sides of this equation by 2 to get x = 40.
the man's age today is 40.
20 years from now, the man's age will be 60.
20 years ago, the man's age was 20.
60 / 20 = 3.
the man's age 20 years from now is 3 times the man's age 20 years ago.
the problem is solved.
the man's age today is 40.


problem 3:


x = the man's age today.
y = the son's age today.
5 years ago, the father's age was 6 times the son's age.
this means that (x-5) = 6 * (y-5).
15 years from now, the father's age will be 2 times the son's age.
this means that (x+15) = 2 * (y+15).
you have two equations that need to be solved simultaneously.
they are:
(x-5) = 6 * (y-5)
(x+15) = 2 * (y+15)
simplify these equations to get:
x - 5 = 6y - 30
x +15 = 2y + 30
subtract the second equation from the first to get -20 = 4y - 60.
add 60 to both sides of this equation to get 40 = 4y.
divide both sides of this equation by 4 to get y = 10.
the son's age today is 10.
the son's age 5 years ago was 5.
the son's age 15 years from now is 25.
you are given that, 5 years ago, the father's age is 6 times the son's age 5 years ago.
5 years ago the son's age was 5.
this means the father's age had to be 30, because 6 * 5 = 30.
this means the father's age today is 35.
the father's age today is 35.
the father's age 5 years ago was 30.
the father's age 15 years from now is 50.
5 years ago, the ratio of the father's age to the son's age was 30/5 = 6.
15 years from now, the ratio of the father's age to the son's age will be 50/25 = 2.
the problem is solved.
the father's age today is 35.