Layla is as old as Miya was four years ago

Key concept: This is an age word problem. Translate each sentence into an equation, then solve for the unknown age step by step.

Step by step

Let Layla's current age be $L$ and Miya's current age be $M$.

Step 1: Translate the first statement

"Layla is as old as Miya was four years ago" means:

$L = M - 4$

Step 2: Translate the second statement

"In two years, Layla’s age will be eleven more than half of Miya’s age" means:

$L + 2 = 11 + \frac{1}{2}(M + 2)$

Step 3: Substitute $M = L + 4$

From the first equation:

$M = L + 4$

Substitute into the second equation:

$L + 2 = 11 + \frac{1}{2}(L + 6)$

Step 4: Solve

Multiply both sides by 2:

$2L + 4 = 22 + L + 6$

$2L + 4 = L + 28$

$L = 24$

Answer

Layla is 24 years old now.

Pitfall alert

A frequent mistake is to use Miya's current age directly in the phrase "Miya was four years ago." That phrase refers to Miya's age four years in the past, so it is $M-4$, not $M+4$.

Another pitfall is forgetting that "in two years" applies to both ages in the second statement.

Try different conditions

If the second sentence had said "Layla’s age will be eleven more than half of Miya’s current age," then the equation would be

$L+2 = 11 + \frac{1}{2}M$

That small wording change would give a different answer, so age problems depend very closely on the exact phrasing.

Further reading

age problem, equation, substitution