SOLUTION: 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

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?
Found 2 solutions by Maths68, ankor@dixie-net.com:
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Present age of mother = m years old
Present age of father = f years old
Present age of John = j years old

Two years hence
mother will be = m+2 years old
John will be = j+2 years old
Then
mother will be twice his age
m+2=2(j+2)
m+2=2j+4
m=2j+4-2
m=2j+2.................(1)

Five years hence
father will be = f+5 years old
John will be = j+5 years old
Then
father will be thrice his present age
f+5=3(j+5)
f+5=3j+15
f=3j+15-5
f=3j+10..................(2)

the sum of all the three ages is 105
m+j+f=105
Put the value of m and f from (1) and (2) to above equation
2j+2+j+3j+10=105
6j+12=105
6j=105-12
6j=93
6j/6=93/6
j=31/2
Put the value of j in (1)
m=2j+2.................(1)
m=2(31/2)+2
m=31+2
m=33
Put the value of j in (2)
f=3j+10..................(2)
f=3(31/2)+10
f=93/2+10
f=(93+20)/2
f=113/2
f=56.5
Difference b/w parents ages = f-m=56.5-33= 23.5 years.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
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