Marisa is changing her dog's food from a puppy formula to an adult formula. The vet recommended that she exchange 2 ounces of adult formula for 3 ounces of puppy formula each day. Her dog usually eats 20 ounces of food per day. After how many days will the dog's daily diet include more adult formula than puppy formula?

a. Write and solve an inequality.

b. Explain the correct domain of the solution set.

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
let me know if you have any questions!