a. every day the dog gets 2 more ounces of adult formula than the previous day. in other words, after day 1, the dog gets 2 ounces of adult formula, after day 2, the dog gets 4 ounces of adult formula, etc. On the other hand, every day the dog gets 3 less ounces of puppy formula than the previous day starting from 20 ounces of puppy formula. this means after day 1 the dog will get 17 ounces of puppy formula, then after day 2 the dog will get 14 ounces of puppy formula, etc.
to generalize, after n days, the dog will have 2n of adult formula and 20-3n of puppy formula. we want the n such that there are more adult formula than puppy formula. in other words, we want:
2n>20 - 3n
solving this inequality yields:
n>4 days
b. this part may seem a little weird but take a close look the right side of the inequality: it represents the number of kid formula after n days. if n is too big, the the right side would be negative!!! we can't let that happen so 20 - 3n>0. solving for n gives:
n<6.67 (make sure you note that n must be an integer).
now look at the left side, n cannot be negative because if it was, the amount of adult formula would be negative. fortunately, that isn't a problem because according to part (a), n is greater than 4 so our domain is:
4<n<6.67 where n is an integer
let me know if you have any questions!
