1)There are 7 groups of Scouts attending a campfire with an average of 28 scouts per group. Each group has a different number of scouts. If the largest group has 33 scouts in it, what is the smallest possible number of scouts in each group?
2)The average amount of money that 5 boys had was $1 more than the average amount of money 4 girls had. After Miss Chan had given $10 to the girls, the boys now had the same total amount as the girls. How much money did the girls have altogether at first?
1) 7 groups * 28scouts/group = 196 scouts
If you take out the largest group, then there are 6 groups with 163 scouts.
Now, we know that no group has more than 32 scouts (assuming that there was only one group with 33, which was not explicitly stated).
So, if we posit 5 groups of 32, that makes 160 scouts, leaving a mere 3 for the smallest group.
If b = the average money per boy, and g for girls, then we are told
b = g+1
Now, the total money for each group is
B = 5b
G = 4g
Adding $10 to the girls,
G+10 = B
4g+10 = B
4g + 10 = 5(g+1)
5 = g
6 = b
Check the answer:
5 boys at $6 = $30
4 girls at $5 = $20
Add $10 to girls, they now also have $30.
So, given all that, what's the answer to the question?
1) To find the smallest possible number of scouts in each group, we need to consider that the largest group has 33 scouts. If the average number of scouts per group is 28, we can calculate the total number of scouts by multiplying the average by the number of groups: 28 x 7 = 196 scouts in total.
Since the largest group has 33 scouts, we can subtract that from the total to find the remaining scouts in the smaller groups: 196 - 33 = 163 scouts.
To find the smallest possible number of scouts in each group, we divide the remaining scouts by the number of smaller groups (which is 6 since we have one group with 33 scouts): 163 / 6 = 27.1667.
Since we can't have a fraction of a scout, we round up to the nearest whole number, which means the smallest possible number of scouts in each group is 28.
2) Let's assume the average amount of money the 4 girls had initially was x. According to the question, the average amount of money the 5 boys had was $1 more than that. So, the average amount of money the boys had was x + $1.
Let's calculate the total amount of money the 4 girls had initially: 4x.
After Miss Chan gave $10 to the girls, the boys had the same total amount of money. This means the total amount of money the boys had originally was also 4x + $10.
Since there are 5 boys, the average amount of money per boy would be (4x + $10) / 5.
We know the average amount per boy is x + $1, so we can equate the two expressions: (4x + $10) / 5 = x + $1.
Let's solve this equation to find the value of x, which represents the initial average amount of money per girl.
Multiplying both sides of the equation by 5 gives us 4x + $10 = 5x + $5.
Rearranging the equation gives us 5x - 4x = $10 - $5, which simplifies to x = $5.
So, the initial average amount of money per girl was $5.
To find the total amount of money the girls had altogether at first, we multiply the average amount per girl by the number of girls: $5 x 4 = $20.
Therefore, the girls had a total of $20 altogether at first.