There are 30 boys and girls in a group. The average height of the children is 145 cm. When 3 more boys joined the group, the average height of each student increased by 0.5 cm. The total height of the girls in the group is 1820 cm. Each of the statements below is either true, false or not possible to tell from the information given. For each statement, put a tick ( $\checkmark$ ) to indicate your answer.

Statement	True	False	Not possible to tell
The average height of the 3 boys who joined the group is 150.5 cm.
The average height of all the boys before the 3 boys joined the group is greater than 145 cm.

1. Calculate the total height of the 30 children initially

$\text{Total height initially} = 30 \times 145 = 4350\text{ cm}$

2. Calculate the new total height after 3 boys joined

$\text{New number of children} = 30 + 3 = 33$
$\text{New average height} = 145 + 0.5 = 145.5\text{ cm}$
$\text{New total height} = 33 \times 145.5 = 4801.5\text{ cm}$

3. Evaluate the first statement by finding the average height of the 3 new boys

$\text{Total height of 3 new boys} = 4801.5 - 4350 = 451.5\text{ cm}$
$\text{Average height of 3 new boys} = 451.5 \div 3 = 150.5\text{ cm}$
Therefore, the first statement is True.

4. Calculate the total height of the boys initially

$\text{Total height of boys initially} = 4350 - 1820 = 2530\text{ cm}$

5. Evaluate the second statement

To find the average height of the boys initially, we need to divide their total height ($2530\text{ cm}$) by the number of boys. Since the exact number of boys in the initial group of 30 is unknown, we cannot calculate their average height. For example, if there were 17 boys, the average would be $2530 \div 17 \approx 148.8\text{ cm}$ (greater than 145), but if there were 18 boys, the average would be $2530 \div 18 \approx 140.6\text{ cm}$ (less than 145).
Therefore, the second statement is Not possible to tell.