Samia is 7 years older than Amina. What are their ages if 1/4 Samia’s age is equal to 1/2 Amina?

 

We denote Amina's age as \(a\) and Samia's age as \(s\). The given data can be represented by two equations:

1. Samia is 7 years older than Amina: \(s = a + 7\)

2. The fraction of Samia's age is equal to half of Amina's age: \(\frac{ 1}{4}s = \frac{1}{2}a\)

Now let's replace the expression for Samia's age in the first equation with the second equation:

\[\frac { 1} {4}(a + 7) = \frac{1}{2}a\]

Multiply both sides by 4 to subtract the fraction:

\[a + 7 = 2a\]

Subtract both sides of

\(a\):

\[7 = a\]

Now that we know Amina's age (\(a = 7\)), we can find Samia's age using the first equation:

\[s = a + 7 \]

\ [s = 7 + 7\]

\[s = 14\]

So Amina is 7 years old and Samia is 14 years old.