First equation:

x + y = 55

for the second equation, I checked to see how many years passed (93-55 = 38, that’s the total for both, so the number of years passed is actually 19)

second equation

x + 19 = y

then we’ll put that into the first equation

x + y = 55

x + (x + 19) = 55

x + x + 19 = 55

2x = 36

x = 36 / 2

x = 18

The son is 18.

Now we go back to our first equation with that info:

x + y = 55

18 + y = 55

y = 55 – 18

y = 37

dad is 37.

Let’s check this one more time against the 93 equation.

x + 19 + y + 19 = 93

x + y = 93 – 19 – 19

x + y = 55

yay it worked. So:

son = 18

dad = 37

I am using F for father and S for son… Hope that makes more sense than X and Y.

F + S = 55 (Father plus Son = 55)

2(F-S)+F+S=93 (2 times the difference between F and S age plus their current ages = 93)

You know that F+S = 55, consequently 2(F-S)+55=93

If you break down that equation, you end up with F – S = 19

Therefore F = 19 + S

Since F+S=55, you can say that 19+S+S=55

So S=18 and F = 37

You can verify this checking the difference in their ages and adding it (twice – once for each of them) to their current ages.

37-18=19

19 x 2 = 38

38 + 37 + 18 = 93

Hope that helps!

y= age of father

in y-x years son will reach present father’s age.

x+y = 55 — (1)

y+y-x+x+y-x=93

3y-x=93 — (2)

from (1) and (2)

4y=148

y=37 father

x=55-37=18 son

check : after 19 years (37-18), son will be 37

son+father = 37+(56)=93

93-55=38 father

55-38=17 son

I don’t know 100% but it makes sense to me.