course Mth 151 I really have a hard time with word problems. ????\???8G??????assignment #008008. `Query 8
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08:06:08 1.3.6 9 and 11 yr old hosses; sum of ages 122. How many 9- and 11-year-old horses are there?
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RESPONSE --> I think first I would find a number divisable by 9. So I would subtract 122 - 5 = 117. 117/9= 13. So there would be 5 but that would only leave 5 yrs and there has to be at least 1 horse 11 yrs old. So by trial and error I substracted 11 from 122, then 22 from 122 and so on until I came up wiht 122-77=45 which is divisable by 11 and 9. So there are 7 horses that are age 11 and 5 horses age 9. 11*7=77 and 5*9=45; 77 + 45 = 122. confidence assessment: 2
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08:06:27 ** If there was one 11-year-old horse the sum of the remaining ages would have to be 122 - 11 = 111, which isn't divisible by 9. If there were two 11-year-old horses the sum of the remaining ages would have to be 122 - 2 * 11 = 100, which isn't divisible by 9. If there were three 11-year-old horses the sum of the remaining ages would have to be 122 - 3 * 11 = 89, which isn't divisible by 9. If there were four 11-year-old horses the sum of the remaining ages would have to be 122 - 4 * 11 = 78, which isn't divisible by 9. If there were five 11-year-old horses the sum of the remaining ages would have to be 122 - 5 * 11 = 67, which isn't divisible by 9. The pattern is 122 - 11 = 111, not divisible by 9 122 - 2 * 11 = 100, not divisible by 9 122 - 3 * 11 = 89, not divisible by 9 122 - 4 * 11 = 78, not divisible by 9 122 - 5 * 11 = 67, not divisible by 9 122 - 6 * 11 = 56, not divisible by 9 122 - 7 * 11 = 45, which is finally divisible by 9. Since 45 / 9 = 5, we have 5 horses age 9 and 7 horses age 11. **
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RESPONSE --> self critique assessment: 2
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08:15:47 Query 1.3.10 divide clock into segments each with same total
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RESPONSE --> Divide it into 6 sections equaling 13. confidence assessment: 1
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08:18:09 ** The total of all numbers on the clock is 78. So the numbers in the three sections have to each add up to 1/3 * 78 = 26. This works if we can divide the clock into sections including 11, 12, 1, 2; 3, 4, 9, 10; 5, 6, 7, 8. The numbers in each section add up to 26. To divide the clock into such sections the lines would be horizontal, the first from just beneath 11 to just beneath 2 and the second from just above 5 to just above 8. Horizontal lines are the trick. You might have to draw this to see how it works. **
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RESPONSE --> I divided it into 6 section equaling 13 in each section. The total is 78. Did I arrive at the answer incorrectly or will it work doing it like this? self critique assessment: 2
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08:25:09 Query 1.3.18 M-F 32 acorns each day, half of all acorns eaten, 35 acorns left after Friday
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RESPONSE --> 1/2 of the acorns were eaten each day so 16 were left each day 16*5=80, 80-35=45 so there were an additional 45 acorns eaten. confidence assessment: 1
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08:26:37 ** You have to work this one backwards. If they were left with 35 on Friday they had 70 at the beginning (after bringing in the 32) on Friday, so they had 70 - 32 = 38 at the end on Thursday. So after bringing in the 32 they had 2 * 38 = 76 at the beginning of Thursday, which means they had 76 - 32 = 44 before the 32 were added. So they had 44 Wednesday night ... etc. **
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RESPONSE --> I see now how to work it. self critique assessment: 1
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08:37:12 Query 1.3.30 Frog in well, 4 ft jump, 3 ft back.
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RESPONSE --> 20 foot well. If he jumps only 1 foot a day it would take him 20 days. confidence assessment: 2
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08:38:11 ** COMMON ERROR: 20 days CORRECTION: The frog reaches the 20-foot mark before 20 days. On the first day the frog jumps to 4 ft then slides back to 1 ft. On the second day the frog therefore jumps to 5 ft before sliding back to 2 ft. On the third day the frog jumps to 6 ft, on the fourth to 7 ft., etc. Continuing the pattern, on the 17th day jumps to 20 feet and hops away. The maximum height is always 3 feet more than the number of the day, and when max height is the top of the well the frog will go on its way. **
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RESPONSE --> I did not add the previous days jump. self critique assessment: 2
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08:44:39 Query 1.3.48 How many ways to pay 15 cents?
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RESPONSE --> 15 pennies; 10 pennies 1 nickle; 1 dime 5 pennies, 1 dime 1 nickle; 3 nickles; 2 nickles 5 pennies, confidence assessment: 3
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08:45:15 10-13-2007 08:45:15 ** To illustrate one possible reasoning process, you can reason this out in such a way as to be completely sure as follows: The number of pennies must be 0, 5, 10 or 15. If you don't use any pennies you have to use a dime and a nickle. If you use exactly 5 pennies then the other 10 cents comes from either a dime or two nickles. If you use exactly 10 pennies you have to use a nickle. Or you can use 15 pennies. Listing these ways: 1 dime, 1 nickel 1 dime, 5 pennies 2 nickels, 5 pennies 3 nickels 15 pennies 1 nickel 10 pennies **
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NOTES -------> You would have to break down pennies, dimes & nickles.
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08:45:18 ** To illustrate one possible reasoning process, you can reason this out in such a way as to be completely sure as follows: The number of pennies must be 0, 5, 10 or 15. If you don't use any pennies you have to use a dime and a nickle. If you use exactly 5 pennies then the other 10 cents comes from either a dime or two nickles. If you use exactly 10 pennies you have to use a nickle. Or you can use 15 pennies. Listing these ways: 1 dime, 1 nickel 1 dime, 5 pennies 2 nickels, 5 pennies 3 nickels 15 pennies 1 nickel 10 pennies **
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RESPONSE --> self critique assessment: 2
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08:55:38 Query 1.3.52 Given 8 coins, how do you find the unbalanced one in 3 weighings
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RESPONSE --> Put 4 on each scale and which ever weight the least of the two you would put on the scale again in stacks of two on each scale and then which ever weight the least of the two stacks you would put one coin on each scale and find the fake one. confidence assessment: 3
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08:56:27 ** Divide the coins into two piles of 4. One pile will tip the balance. Divide that pile into piles of 2. One pile will tip the balance. Weigh the 2 remaining coins. You'll be able to see which coin is heavier. **
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RESPONSE --> You do it by dividing the coins to begin with. self critique assessment: 2
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