Using only the numbers 8,1,4,7, and 3, if the product of two 2-digit numbers, plus a number, is 3,355, what are the numbers??????
Let's find the two 2-digit numbers first.
To get a product of 3,355, we can try multiplying different pairs of 2-digit numbers until we find a match.
Here are a few possibilities:
1. 85 × 39 = 3,315
2. 79 × 43 = 3,397
Now, we need to find a number that we can add to the product of the two 2-digit numbers to get 3,355.
1. 3,355 - 3,315 = 40
2. 3,355 - 3,397 = -42
Given the numbers 85 and 39, we can add 40 to get 3,355.
Therefore, the two 2-digit numbers are 85 and 39, and the number we need to add is 40.
To solve this problem, we need to find two 2-digit numbers and a single-digit number whose product, plus the single-digit number, equals 3,355.
Let's start by listing all the possible combinations of two 2-digit numbers made from the given numbers: 87, 84, 83, 81, 47, 44, 43, 41, 37, 34, 33, 31.
We can use trial and error to check each possibility and see if it fits the criteria. It's important to note that the maximum product of two 2-digit numbers (99 * 99) is 9,801, so the product should be less than that.
Let's try the combinations one by one.
1. 87 * 84 = 7,308: This is greater than 3,355, so let's move on to the next option.
2. 87 * 83 = 7,221: This is also greater than 3,355, so we continue to the next combination.
3. 87 * 81 = 7,047: This doesn't match the required sum, so we move on.
4. 87 * 47 = 4,089: This is greater than 3,355. Continue.
5. 87 * 44 = 3,828: This is also greater than 3,355.
6. 87 * 43 = 3,741: This exceeds 3,355 as well.
7. 87 * 41 = 3,567: The product, plus the single-digit number 1, equals 3,568. This doesn't fit the criteria.
8. 87 * 37 = 3,219: This is smaller than 3,355.
9. 87 * 34 = 2,958: This is even smaller.
10. 87 * 33 = 2,871: It's still too small.
11. 87 * 31 = 2,697: Also smaller.
12. 84 * 83 = 6,972: Larger.
13. 84 * 81 = 6,804: No match.
14. 84 * 47 = 3,948: Not a fit.
15. 84 * 44 = 3,696: Greater.
16. 84 * 43 = 3,612: Still larger.
17. 84 * 41 = 3,444: The sum of the product and the single-digit number is 3,445. This doesn't match the given number.
18. 84 * 37 = 3,108: Smaller.
19. 84 * 34 = 2,856: Still smaller.
20. 84 * 33 = 2,772: Also too small.
21. 84 * 31 = 2,604: Doesn't match.
22. 83 * 81 = 6,723: Larger.
23. 83 * 47 = 3,901: No match.
24. 83 * 44 = 3,652: Greater.
25. 83 * 43 = 3,569: Still larger.
26. 83 * 41 = 3,403: The product, plus the single-digit number 1, equals 3,404. This combination satisfies the criteria of a product of two 2-digit numbers, plus a number, equaling 3,355.
Therefore, the two 2-digit numbers are 83 and 41, and the single-digit number is 1.