(1) The mean age of five children is 8 years 4 months. When Amina joins the children, their mean age becomes 8 years 5 month How old is Amina?

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To find Amina's age, we can follow these steps:

1. **Convert the mean ages into a single unit (months)**:
   - The mean age of the five children is 8 years 4 months, which can be converted to months:
     $$
     8 \text{ years} = 8 \times 12 = 96 \text{ months}
     $$
     $$
     8 \text{ years} 4 \text{ months} = 96 + 4 = 100 \text{ months}
     $$
   - The mean age of the six children (after Amina joins) is 8 years 5 months:
     $$
     8 \text{ years} 5 \text{ months} = 96 + 5 = 101 \text{ months}
     $$

2. **Calculate the total age of the five children**:
   - Since the mean age of the five children is 100 months, the total age of the five children is:
     $$
     \text{Total age of 5 children} = 5 \times 100 = 500 \text{ months}
     $$

3. **Calculate the total age of the six children**:
   - The mean age of the six children is 101 months, so the total age of the six children is:
     $$
     \text{Total age of 6 children} = 6 \times 101 = 606 \text{ months}
     $$

4. **Find Amina's age**:
   - Amina's age can be found by subtracting the total age of the five children from the total age of the six children:
     $$
     \text{Amina's age} = \text{Total age of 6 children} - \text{Total age of 5 children}
     $$
     $$
     \text{Amina's age} = 606 - 500 = 106 \text{ months}
     $$

5. **Convert Amina's age back to years and months**:
   - To convert 106 months into years and months:
     $$
     106 \text{ months} = 8 \text{ years} \text{ and } 10 \text{ months} \quad (\text{since } 106 \div 12 = 8 \text{ remainder } 10)
     $$

Thus, Amina is **8 years and 10 months old**.
Amina is 8 years and 10 months old.

(1) The mean age of five children is 8 years 4 months. When Amina joins the children, their mean age becomes 8 years 5 month How old is Amina?

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