A mother is currently 30 years older than her son. 5 years from now the mother will be 4 times as old as the son. what is the current age of the son

Answer 1

Step 1: Create an equation based on the future ages

In 5 years, the son will be x+5 years old, and the mother will be (x+30)+5=x+35 years old. According to the problem, in 5 years, the mother will be 4 times as old as her son. This gives the equation: x+35=4(x+5)

Step 2: Solve the equation

Now, let's solve for x. To solve this, we need to simplify and isolate x (the son's current age).

Expand the right-hand side of the equation:

x+35=4(x+5)

Apply the distributive property to expand 4(x+5):

x+35=4x+20

Move the terms involving x to one side of the equation. Subtract x from both sides:

35=3x+20

Isolate the constant term. Subtract 20 from both sides to move the constants to one side:

35−20=3x

Simplifying gives:

15=3x

Solve for x by dividing both sides by 3:

x= \frac{15}{3} = 5

So, the son's current age is x=5.

Step 3: Verify the solution

The current age of the son is 5 years. The mother is currently 5+30=35 years old. In 5 years, the son will be 5+5=10 years old, and the mother will be 35+5=40 years old. Indeed, 40 is 4 times 10, so the solution is correct.

Answer 2

Given:

(1) Son's Age = x

(2) Mother's Age = 30 +x

In 5 years, the mother's age will be 30 + 5 + x = 4(x+5). Now, we solve for x to find the son's age:

35 + x = 4x +20

15 = 3x

x = 5

The son's current age is 5 years old.

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