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Mr. olsen has classified the charities to which he gives money to into 3 different groups. Each charity in the 1st. group will get \$1 . Each charity in the 2 nd. group will get 9 times as much or \$9 . Each in the 3 rd. will get 9 times as much as each in the 2 nd. groups or \$81 . he never gives to more than 8 charities in each group . one week he gave \$200. How many charities received money from him?

1*ch1 + 9*ch2 + 81*ch3 = 200

with ch1+ch2+ch3 <= 8

where ch1 is the number of charities belonging to the first group, ch2 is the number of charities belonging to the second group, and ch3 is the number of charities belonging to the 3rd group

the number in charity 3 can only be 1 or 2; if the number is 1, then there has to be at least 13 charities in group 2; therefore this possibility is excluded.

ch3 = 2

If ch3=2, ch2 can be 1,2,3,or 4

If ch2 = 4, then ch1 = 2

and 4+2+2 = 8

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