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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?

  • maths -

    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?

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