Consider the question. An elementary school teacher is making Halloween goodie bags for her class. She wants the bags to be personalized, so she surveys her students asking whether they'd like a vampire-themed bag or a pumpkin-themed bag. Of her 25 students, 11 indicate they want the vampire-themed bag and 14 indicate they want the pumpkin-themed bag. The store the teacher shops at sells packs of 5 of each theme at a price of $3 per package, as well as individual bags of each theme at a price of $1 each. What is the least amount of money the teacher can spend on the bags if she buys every student the theme they requested?
If the answer is '17'; explain the reasoning:
Because it is cheaper to buy the packs of 5, the teacher should satisfy the 11 students who want the vampire theme with 2 packs of 5 and 1 individual bag. This will cost the teacher 2 * 3 + 1 * 1 = $7. Similarly, the 14 students who want a pumpkin - themed bag can be satisfied by 2 packs of 5 and 4 individual bags at a cost of 2 * 3 + 4 * 1 = $10. Therefore, the teacher must spend 7 + 10 = $17.