Rob must be new here...
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A simpler way to think about this is that each horse you buy puts you $9 in the hole ($10 for 1 animal) and each set of ducks you buy puts you 7 animals ahead ($1 for 8 animals). To get your answer, just find the least common multiple of 7 and 9 (63). This means you would need to get $63 behind buying horses (i.e. 7 of them) and 63 ducks ahead (i.e. buy 9 sets of them) then spend the rest of your money on goats since they are 1-for-1.context