Johnny is one-third old as his sister, Mary, and 8 years younger than his brother Logan. The sum of their ages is 38 years old. How old is Johnny?

Johnny' age ---- x

Mary's age ----- 3x , (x is one third of 3x)
logan ---- x+8

x + 3x + x+8 = 38

solve for x

Well, Johnny seems to be in a bit of a pickle! Let's use some clown math to figure this out.

Let's say Mary's age is M, Logan's age is L, and Johnny's age is J. According to the information given:

J = (1/3)M (Johnny is one-third as old as Mary)
J = L - 8 (Johnny is 8 years younger than Logan)
M + L + J = 38 (the sum of their ages is 38)

Now, let's put on our clown noses and solve this hilarious puzzle!

Since J = (1/3)M and J = L - 8, we can substitute L - 8 for J in the first equation:

(1/3)M = L - 8

Now, let's substitute (1/3)M for J in the third equation:

M + L + (1/3)M = 38

Combining like terms, we get:

(4/3)M + L = 38

To make this equation even funnier, let's multiply everything by 3 to get rid of the fractions:

4M + 3L = 114

We also know that J = (1/3)M, so let's substitute (1/3)M for J in the second equation:

(1/3)M = L - 8

Now, let's substitute (1/3)M for J in the equation we got rid of the fractions:

(1/3)M = L - 8

Multiply everything by 3 to get rid of the fractions:

M = 3L - 24

Now, let's solve this funny system of equations!

We have two equations:

4M + 3L = 114 and M = 3L - 24

We can substitute 3L - 24 for M in the first equation:

4(3L - 24) + 3L = 114

Distributing and combining like terms:

12L - 96 + 3L = 114

15L - 96 = 114

Adding 96 to both sides:

15L = 210

Dividing both sides by 15:

L = 14

Now that we know Logan's age is 14, we can substitute it back into the equation M = 3L - 24:

M = 3(14) - 24

M = 42 - 24

M = 18

Lastly, we can substitute M = 18 back into the equation J = (1/3)M:

J = (1/3)(18)
J = 6

So, after all that silly clown math, it turns out Johnny is 6 years old!

Let's use algebra to solve this problem step by step.

Let's assume Johnny's age is x.

According to the problem, Mary's age is three times Johnny's age, so Mary's age is 3x.

The problem also states that Logan's age is 8 years older than Johnny's age, so Logan's age is x + 8.

The sum of their ages is 38, so we can write the equation:

x + 3x + (x + 8) = 38

Simplifying this equation, we get:

5x + 8 = 38

Subtracting 8 from both sides, we get:

5x = 30

Dividing both sides by 5, we get:

x = 6

Therefore, Johnny is 6 years old.

To find Johnny's age, we can set up a system of equations based on the given information.

Let's assume that Johnny's age is J, Mary's age is M, and Logan's age is L.

We know that Johnny is one-third as old as Mary, so we can write the equation:

J = (1/3)M

We also know that Johnny is 8 years younger than Logan, so we can write the equation:

J = L - 8

Finally, the sum of their ages is 38 years old, so we can write the equation:

J + M + L = 38

Now we can solve this system of equations to find their ages.

First, substitute the value of J from the second equation into the third equation:

(L - 8) + M + L = 38

Combine like terms:

2L + M - 8 = 38

Next, substitute the value of J from the first equation into the second equation:

(1/3)M = L - 8

Multiply both sides of the equation by 3 to eliminate the fraction:

M = 3L - 24

Now substitute the value of M from the second equation into the first equation:

J = (1/3)(3L - 24)

Simplify:

J = L - 8

Now we have a system of two equations with two variables:

2L + M = 46 (Equation 1)
L - M = 8 (Equation 2)

We can solve this system of equations using substitution or elimination.

I'll use elimination to solve the system:

Multiply Equation 2 by -1 to change the sign:

-L + M = -8 (Equation 3)

Add Equation 1 and Equation 3:

2L + M - L + M = 46 - 8

Combine like terms:

L + 2M = 38 (Equation 4)

Now we have a system of two equations with two variables:

L + 2M = 38 (Equation 4)
L - M = 8 (Equation 2)

We can solve this system of equations using elimination.

Multiply Equation 2 by 2 to make the coefficients of L the same:

2L - 2M = 16 (Equation 5)

Now, add Equation 4 and Equation 5:

L + 2M + 2L - 2M = 38 + 16

Combine like terms:

3L = 54

Divide both sides of the equation by 3:

L = 18

Now that we know the value of L, we can substitute it back into Equation 2 to find M:

18 - M = 8

Subtract 18 from both sides:

-M = -10

Divide both sides of the equation by -1:

M = 10

Finally, substitute the values of L and M back into Equation 1 to find J:

2(18) + 10 = 46

Simplify:

36 + 10 = 46

Therefore, Johnny is 10 years old.