Question 636780
 Two years hence, John's mother will be twice his age.
Five years hence his father will be thrice his present age.
What is the difference between the ages of his parents,if the sum of all the
 three ages is 105?
:
let j = John's present age
let m = mother's present age
let f = father's present age
:
write an equation for each statement:
:
" Two years hence, John's mother will be twice his age."
m + 2 = 2(j+2)
m + 2 = 2j + 4
m = 2j + 4 - 2
m = 2j + 2
:
"Five years hence his father will be thrice his present age."
Note that it says "PRESENT AGE"
f + 5 = 3j
f = 3j - 5
:
"the sum of all the three ages is 105?"
j + m + f = 105
replace m with (2j+2); replace f with (3j-5)
j + (2j+2) + (3j-5) = 105
6j - 3 = 105
6j = 105 + 3
6j = 108
j = 108/6
j = 18 is John's present age
then
f = 3(18)-5
f = 49 yrs is Father's age
and
m = 2(18) + 2
m = 38 is Mother's age
:
"What is the difference between the ages of his parents,"
49 - 38 = 11 yrs, probably a story here.
:
:
Check this
18 + 38 + 49 = 105