Final answer:
Jana needs to buy at least 16 cookies, a combination of peanut butter and chocolate chip cookies, within her given budget.
Step-by-step explanation:
Jana needs to buy at least 15 cookies and can spend at most $42. Peanut butter cookies cost $2 each and chocolate chip cookies cost $3 each.
To find the minimum number of cookies Jana needs to buy, we can start by assuming she buys all peanut butter cookies. At $2 each, she would need to buy at least 15/2 = 7.5 cookies. Since she can't buy a fraction of a cookie, she needs to buy at least 8 peanut butter cookies.
The cost of buying 8 peanut butter cookies would be 8 * $2 = $16. Since Jana can spend at most $42, she can spend $42 - $16 = $26 on chocolate chip cookies.
Chocolate chip cookies cost $3 each, so Jana can buy at most $26/$3 = 8.666666666666666 cookies. Since she can't buy a fraction of a cookie, she can buy at most 8 chocolate chip cookies.
In total, Jana will buy at least 8 peanut butter cookies and at most 8 chocolate chip cookies. This means she will buy a minimum of 8 + 8 = 16 cookies.
Therefore, Jana needs to buy at least 16 cookies.