A man is 20 years older than his son.if the sum of their ages is 50 years, find their ages ?
you take the difference of their ages, 20, away from the total of their ages, 50, (which leaves 30) and then divide the rest of the years between them, that's 15 each.
M = S + 20
M + S = 50
Substitute S+20 for M in the second equation and solve for M. Insert that value into the first equation to solve for S. Check by putting both values into the second equation.
Let's solve the problem step by step.
Step 1: Assign variables.
Let's represent the son's age with "x". Since the man is 20 years older than his son, the man's age can be represented as "x + 20".
Step 2: Set up the equation.
The sum of their ages is 50 years. So, we can write the equation as:
x + x + 20 = 50
Step 3: Solve the equation.
Combining like terms, we get:
2x + 20 = 50
Subtracting 20 from both sides of the equation, we get:
2x = 30
Dividing both sides of the equation by 2, we get:
x = 15
Step 4: Find their ages.
Now that we have the value of "x" as 15, we can find their ages.
Son's age = x = 15 years
Man's age = x + 20 = 15 + 20 = 35 years
So, the son is 15 years old and the man is 35 years old.
To find the ages of the man and his son, let's set up a system of equations based on the given information:
Let's call the son's age "x" and the man's age "y".
1) The man is 20 years older than his son:
y = x + 20
2) The sum of their ages is 50 years:
x + y = 50
Now we have a system of two equations.
To solve for their ages, we can use the method of substitution or elimination.
Method 1: Substitution
Step 1: Substitute the value of y from Equation 1 into Equation 2:
x + (x + 20) = 50
Step 2: Simplify the equation:
2x + 20 = 50
Step 3: Subtract 20 from both sides:
2x = 30
Step 4: Divide both sides by 2:
x = 15
Step 5: Substitute the value of x back into Equation 1 to find y:
y = 15 + 20
y = 35
Therefore, the son is 15 years old, and the man is 35 years old.
Method 2: Elimination
Step 1: Subtract Equation 2 from Equation 1:
(x + 20) - (x) = 50 - x
Step 2: Simplify and solve for x:
20 = 50 - x
x = 30
Step 3: Substitute the value of x back into Equation 2 to find y:
30 + y = 50
y = 20
Again, we find that the son is 15 years old, and the man is 35 years old.
Both methods give us the same answer: the son is 15 years old, and the man is 35 years old.