Answer this question:Missy had a giant piggy bank in her bedroom. Every day she would search the house for change to put in her bank. After 4 years, the bank was opened and it contained $450 in change. If the second, third, and fourth-year she doubled the amount of money she put in the bank from the amount she had put in the previous year, how much money, in dollars, did she put in the bank the first year?
We let x be the amount of money she put in the bank the first year,. Then the second year was 2 * x,. and the third year was 2 * 2 * x = 4 * x,. and the fourth year was 2 * 2 * 2 * x = 8 * x. And the total amount she put in the bank, $450, is the sum of all four years, or $450 = x + (2 * x) + (4 * x) + (8 * x). This simplifies to $450 = 15 * x. And therefore, the amount of money she put in the bank the first year was x = $30.
The answer is 30.

Answer this question:The teacher agrees to order pizza for the class. For every student in the class, she will buy 2 pieces of cheese and 1 piece of onion and they will eat exactly that amount. A large pizza has 18 slices. She orders 6 total pizzas and there are 8 pieces of cheese and 4 pieces of onion leftover. How many students are in the class?
Cheese pizzas are 2 / 3 of the pizza's purchased because 2 / (2 + 1) = 2 / 3. She buys 4 cheese pizzas because 6 x (2 / 3) = 4. These give her 72 pieces of cheese pizza because 4 x 18 = 72. The students at 64 pieces of cheese because 72 - 8 = 64. There are 32 students in her class because 64 / 2 = 32.
The answer is 32.

Answer this question:Tom receives a $12 allowance per month. In the first week, he spends a third of it; in the second week, he spends a quarter of what he has left. How much money does he have left to finish the month?
The first week he spends: $12 * 1 / 3 = $4. So he has $12 - $4 = $8 left. In the second week, he spends $8 x 1 / 4 = $2. So Tom has $8 - $2 = $6 left to finish the month.
The answer is 6.

Answer this question:Katerina purchases 3 pots and 4 pans at the home goods store. Each pot costs $20. The total cost of Katerina's items is $100. If each pan is the same price, what is the cost of 2 pans?

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
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The cost of the pots is 3 * $20 = $60. The cost of 4 pans is $100 - $60 = $40. Since each pan is the same price, the cost of 1 pan is $40 / 4 = $10. The cost of 2 pans is $10 + $10 = $20.
The answer is 20.