The sum of the ages of Frank and John is 54 years. 2 years ago, Frank was 4 times as old as John. Find John's age.

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enotechris's profile pic

enotechris | College Teacher | (Level 2) Senior Educator

Posted on

Right now, Frank + John = 54.

1)  F + J = 54

But 2 years ago, Both Frank and John were 2 years younger each, which meant the sum of their ages is different by 4 years

2)  F + J = 54 - 4 = 50

And 2 years ago, Frank was 4 times older than John

3)  F = 4J

If we substitute eq. 3 for F in eq 2, we have

4)  4J + J = 50

5)  5J = 50

6)  J = 10

But John was 10 2 years ago, so now his age is 12. Substituting his current age in eq. 1

7)  F + 12 = 54

8)  F = 42, so currently Frank is 42 and John is 12. Two years ago, Frank was 40 and John 10.

givingiswinning's profile pic

givingiswinning | Student, Grade 10 | (Level 1) Valedictorian

Posted on

F + J = 54

54 - 4 = 50

F + J = 50

4J = F

4j + j = 54

5j = 50

j = 10

  • J = 12   

F + 12 = 54

  • F = 42
atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

The sum of the ages of Frank and John is 54 years. 2 years ago, Frank was 4 times as old as John. Find John's age.

F + J = 54

2 years ago both F and J were 2 years younger: 2 + 2 =4 so we subtract that from 54:

54 - 4 = 50

so 2 years ago the sum of their age was 50. 

F + J = 50

We then find out F is 4 times as old as J so:

4J = F

since we know F = to 4j we plug in 4j as f  into the F + J = 50 problem:

4j + j = 54

add the like terms:

5j = 50

divide by 5:

j = 10

now we add the 2 years we took off:

J = 12   

we now know J is 12 so plug it into the first equation and solve:

F + 12 = 54

subtract 12:

F = 42

John is 12 and Frank is 42

revolution's profile pic

revolution | College Teacher | (Level 1) Valedictorian

Posted on

Right now, F+J = 54 years

But two years ago, both of them were two years younger than now, so the sum of their age would be different by four years, so:

F+J= 54-4=50 years - eqn 1

Also, Frank was four times as old as John so:

F= 4J - eqn 2

Sub eqn 2 to eqn 1

4J+J=50

5J=50

J=10 years

Since John was age of 10 two years earlier, so his present age would be 10+2= 12 years.

So, now the earlier eqn would look like that

F+12=54

F+12-12=54-12

F=42. Thus, frank is 42 years of age while John is 12 years of age.

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