Ruby is 10 years older than Sam. The sum of their ages is 52. How old is Sam?

s=sams age

s+s+10=52
2s=-10+52
2s=42
s=42/2
S=21

s = Sam's age

s + s + 10 = 52

2s = 42

s - 21

Let's solve this step-by-step.

Step 1: Let's assume Sam's age as 'S'.
So, Ruby's age will be 'S + 10' (as Ruby is 10 years older than Sam).

Step 2: The sum of their ages is given as 52.
So, we can write the equation as:
S + (S + 10) = 52

Step 3: Solve the equation:
2S + 10 = 52
2S = 52 - 10
2S = 42
S = 42 / 2
S = 21

Therefore, Sam is 21 years old.

To find out Sam's age, we can solve the problem by using equations.

Let's assume that Sam's age is represented by the variable "x."

According to the problem, Ruby is 10 years older than Sam. So, we can represent Ruby's age as "x + 10."

The sum of their ages is given as 52. Therefore, we can establish the equation:

x + (x + 10) = 52

Now, we can solve this equation to find the value of x, which will give us Sam's age.

Combining like terms, we have:

2x + 10 = 52

Subtracting 10 from both sides of the equation:

2x = 42

Dividing both sides of the equation by 2:

x = 21

Therefore, Sam is 21 years old.