Two years ago a father was four times as old as his son. Three years from now the father will be only three times as old as the son. How old is each now?
If x represents the son's age two years ago, which expression represents his father's age three years from now?
3x + 15
3x + 3
x + 3
If x represents the son's age two years ago, then the son is currently x + 2 years old.
Two years ago, the father was four times as old as his son, so the father was 4(x).
To determine the current age of the father, we need to add two years to the father's age two years ago (4x + 2).
Three years from now, the father will be (4x + 2) + 3 = 4x + 5 years old.
Therefore, the expression that represents the father's age three years from now is 4x + 5.
Let's solve the problem step-by-step.
1. Let's assume the son's age two years ago is x. Therefore, the son's current age is x + 2.
2. Two years ago, the father was four times as old as his son, so the father's age at that time would be 4x.
3. Three years from now, the son's age will be x + 2 + 3 = x + 5.
4. If x represents the son's age two years ago, then x + 5 represents the son's age three years from now.
5. Since the father will be three times as old as the son three years from now, the father's age would be 3(x + 5).
Hence, the expression that represents the father's age three years from now is 3(x + 5), which simplifies to 3x + 15.
Therefore, the correct expression is 3x + 15.
To solve the problem, let's first represent the son's current age as "x" and the father's current age as "y."
Given: Two years ago, the father was four times as old as his son.
This can be expressed as: y - 2 = 4(x - 2)
Given: Three years from now, the father will be only three times as old as the son.
This can be expressed as: y + 3 = 3(x + 3)
Now we have two equations:
y - 2 = 4(x - 2)
y + 3 = 3(x + 3)
To find the values of x and y, we need to solve this system of equations.
Let's solve for y in the first equation:
y - 2 = 4(x - 2)
y - 2 = 4x - 8
y = 4x - 8 + 2
y = 4x - 6
Now substitute this expression for y in the second equation:
(4x - 6) + 3 = 3(x + 3)
4x - 3 = 3x + 9
4x - 3x = 9 + 3
x = 12
Now we know the son's age is x = 12. To find the father's age, substitute this value back into either equation.
y = 4x - 6
y = 4(12) - 6
y = 48 - 6
y = 42
Therefore, the son's current age is 12, and the father's current age is 42.