Final answer:
To find the mean number of coins for the girls, the total coins for all children are calculated and then the coins that the boys have are subtracted to find the total coins for the girls. The mean for the girls is then calculated by dividing their total coins by the number of girls, resulting in the mean number of coins for the girls being 18.
Step-by-step explanation:
The question asks us to work out the mean number of coins for the girls, given that the overall mean is 15 coins, and the mean for boys is 13 coins with the number of boys being 12.
Step 1: Calculating Total Coins
First, we calculate the total number of coins for all children:
- Total children = Boys + Girls = 12 + 8 = 20
- Mean number of coins for all children = 15
- Total coins for all children = Mean × Total children = 15 coins × 20 children = 300 coins
Step 2: Calculating Total Coins for Boys
Next, we calculate the total number of coins that boys have:
- Mean number of coins for boys = 13
- Total coins for boys = Mean for boys × Number of boys = 13 coins × 12 boys = 156 coins
Step 3: Calculating Total Coins for Girls
By subtracting the boys' coins from the total, we get the total coins for girls:
- Total coins for girls = Total coins for all children - Total coins for boys = 300 coins - 156 coins = 144 coins
Step 4: Calculating Mean for Girls
Finally, we find the mean number of coins for girls:
- Mean for girls = Total coins for girls ÷ Number of girls = 144 coins ÷ 8 girls = 18 coins
Therefore, the mean number of coins for the girls is 18 coins.