Age...3

[nycmathguy]

Tell me about the set up.

John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John now?

John's father's age now = 5(2x)

John's age now = 2x

Alice's age now = x

5(2x) + 2x + x = 58

You say?

 

[MathLover1]

incorrect

should be:

John’s father is 5 times older than John
let father’s age be x
father=5john=> john=x/5

and John is twice as old as his sister Alice.
john=2Alice=> Alice=john/2=>(x/5)/2=x/10

=>father=5*2Alice=10alice =>Alice=x/10

In two years time,

father’s age will be x+2, John’s age will be x/5+2, and Alice will be x/10+2

if the sum of their ages will be 58, we have

x+2+x/5+2+x/10+2=58
x=40=> father is 40 old now
John=x/5=40/5=8=> John is 8 old now
Alice=x/10=40/10=4=> Alice is 4 old now

check:

father is 40 old now-> in two years he will be 42
John is 8 old now-> in two years he will be 10
Alice is 8 old now-> in two years she will be 6

so, 42+10+6=58

 

[nycmathguy]

incorrect

should be:

John’s father is 5 times older than John
let father’s age be x
father=5john=> john=x/5

and John is twice as old as his sister Alice.
john=2Alice=> Alice=john/2=>(x/5)/2=x/10

=>father=5*2Alice=10alice =>Alice=x/10

In two years time,

father’s age will be x+2, John’s age will be x/5+2, and Alice will be x/10+2

if the sum of their ages will be 58, we have

x+2+x/5+2+x/10+2=58
x=40=> father is 40 old now
John=x/5=40/5=8=> John is 8 old now
Alice=x/10=40/10=4=> Alice is 4 old now

check:

father is 40 old now-> in two years he will be 42
John is 8 old now-> in two years he will be 10
Alice is 8 old now-> in two years she will be 6

so, 42+10+6=58

I got 4/5 right. Not too bad. Thanks for correcting my work.