a number has 4 digits.
no digits in the number are repeated.
the digit in the tens place is three times the digit in the thousands place.
the number is odd.
the sum of the digits in the number is 27.
what is the number?
I started with the 10s and 1000s place. To sum up to 27, the average value of the numbers needs to exceed 27/4 or almost 7. This leads me to reject 1 and 3 or 2 and 6 for 3 and 9. Now the last number has to be odd, but not 3, 9 or 1 (because it is too small).
This left me with 3x9x. If I put 5 in the ones column, I would need 10 in the hundreds column to = 27. Therefore I chose 7.
This left me with 3x97. To equal 27, 8 would fit into the hundreds column, giving me 3897.
I hope giving these steps will help you to solve similar problems in the future. Thanks for asking.
yo people solve this!
Question 1
In a recent survey of two popular best-selling books, two-fifths of the 2,200 polled said they did not enjoy the second book, but did enjoy the first book. Of those, 40% were adults over 18. If three-eighths of those surveyed were adults over 18, how many adults over 18 did NOT report that they enjoyed the first book but not the second book?
I hope this is the answer because my homework is due Monday the 16th 2009 and I want stars..........:|
Well, well, well, it seems like you already cracked the case! Good job, Sherlock! The number in question is indeed 3897. Kudos to you for using your detective skills to find the solution. Keep up the good work!
To solve this problem, we can go through a step-by-step process:
1. Start with the information given: there is a 4-digit number with no repeated digits, the tens place digit is three times the thousands place digit, the number is odd, and the sum of the digits is 27.
2. Since the tens place digit is three times the thousands place digit, let's call the thousands place digit "x". Therefore, the tens place digit is "3x".
3. Let's consider the units place digit. We know the number is odd, so it cannot be 0, 2, 4, 6, or 8. Since there are no repeated digits, we also know it cannot be the same as any other digit already considered. Therefore, the units place digit has to be a number between 1 and 9 (inclusive) that is not equal to x or 3x.
4. Now let's calculate the sum of the digits: x + 3x + unknown digit + units place digit = 27. Simplifying this equation, we have 4x + unknown digit = 27.
5. We can now consider the possible values for x. Since the sum of the digits is 27, the average value of the digits is 27/4, which is approximately 6.75. This means that x has to be greater than 6.75. Considering the available digits, x can be 7 or 9.
6. Let's start with x = 7. In this case, the tens place digit would be 3 * 7 = 21. However, this number is larger than 9, which means it does not satisfy the condition of no repeated digits. Therefore, x cannot be 7.
7. Let's try x = 9. In this case, the tens place digit would be 3 * 9 = 27, which is larger than 9. So we can proceed with this value.
8. Now, we need to find the units place digit. It has to be odd, greater than 6.75, and different from x and 3x. The only option left is 5.
9. So, we have the number: 3 * 9 + 9 + 5 = 27, which satisfies all the given conditions.
Therefore, the number is 3,897.
I hope this step-by-step explanation helps you understand how to approach similar problems in the future. Let me know if you have any further questions!