Answers to week 1 problems

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1. Using only pennies, nickels, dimes, and quarters, how many different ways can you make 37 cents?
24

2. Sasha stood at the bottom of a stair case. She had to take 10 steps up to get to the top. Each stair step had a height of 12 inches and a depth of 9 inches. When she arrived at the top of the stairs, how far was she from where she started at the bottom. YOU MUST EXPRESS YOUR ANSWER IN FEET as a decimal to the tenths place. So something like 17.2 (but that of course isn’t it)
12.5

3. 124 in base 5 is equal to what number in base 3. 124₅= _____₃If you don’t know what bases are, watch the video this week 😃. (for a hint though we live in a “base 10 world” where place values are powers of 10). Do not include the subscript for the base 3 in your answer. Just include the numbers that precede the subscript. So for example if your answer was 2121₃ then you would just type in 2121 (that’s not the actual answer by the way 😃).
1110

4. Bob can paint a house in 10 hours. Yao can paint a house in 5 hours. If they work together, how long MANY MINUTES will it take them to paint a house. Must express your answer in minutes. For example, if you thought the answer was 65 minutes (which it isn’t), you would put 65 as your answer. You should NOT put 1 hour 5 minutes.
200

5. Juan has five times as many girlfriends as Pedro. Carlos has one girlfriend less than Pedro. If the total number of girlfriends for the three dudes is 20. How many girlfriends does Pedro have? Be careful when inputting your answer to only put the amount for Pedro. (This problem is brought to you directly from a 1988 Academy Award winning movie. )
3

6. What is the sum of the digits for the # of diagonals of a 14 sided polygon? Again, be careful to follow directions. If you think a 14 sided polygon has 98 diagonals (which it doesn’t), then you would put 17 in for your answer.

14

7. Chickens cost $3 each. Pigs cost $4 each. Ben spent $57 on 16 animals (only chickens and pigs). How many chickens did he buy? Again, be careful. Only put in the # of chickens for your answer.
7

8. What is the sum of the first 50 odd positive integers?
2500

9. Jasmine is obsessed with having exactly a 90 average on her tests. She will have a total of 5 tests for her semester. Her first 4 test scores were 87, 91, 88, and 89. What score does she need on her fifth test to achieve her goal of having exactly a 90 average?

95

10. If x@y = 2x-3y. What is the value of 3@(4@5)?
27

11. A triangle is inscribed in a semicircle that has a diameter of 17 inches.
If the length of line segment BC is equal to 8 inches. How many square inches are in the area of the triangle? Remember to just put in the number of square inches for your answer. Do not put units. So if you thought the answer was 10 square inches (which it isn’t), you would just put 10 into the answer box.

60

12. Rajon had some money. He gave 80% of his money to Eliza. Then Eliza took what she was given, and gave 60% of it to Chet. Chet ended up with what percentage of the original money that Rajon started with? For your answer, do not include the percent sign. Thus if you think the answer is 23% (which it isn’t). You would just type 23 into the box.
48

13. How many positive integer factors does 240 have?

20

14. Coach LaSorda is making a batting order for a wiffle-ball game. He has 7 players to choose from but only 4 can bat in the batting order. How many different permutations (batting orders) can he make?
840

15. What is the units digit (ones digit) of 650 ? (that’s 6 to the 50th power)
6


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