Using only the numbers 8, 1, 4, 7, & 3, the product of 2 two digit numbers plus a number is 3,355?
To find two-digit numbers that, when multiplied together and added to another number, give a total of 3,355, we can use a trial and error method.
Let's start by assuming the first two-digit number is XY, where X represents the tens digit and Y represents the ones digit. The second two-digit number can be represented as AB, where A represents the tens digit and B represents the ones digit. The remaining number can be represented as C.
So, the equation can be written as:
XY * AB + C = 3,355
Since there are no restrictions on the combination of digits to form the two-digit numbers, we will consider all possible combinations.
Let's break down the given numbers (8, 1, 4, 7, and 3) into two sets of digits: {8, 1, 4} and {7, 3}.
Now, let's consider different combinations of digits from the first set to form XY and AB.
Possible combinations for XY:
- 81
- 18
- 14
- 41
- 84
- 48
Possible combinations for AB:
- 74
- 47
- 34
- 43
- 37
- 73
Now, substitute these values in the equation XY * AB + C = 3,355 and calculate the product for each combination:
- For XY = 81 and AB = 74:
81 * 74 + C = 3,355
5,994 + C = 3,355
C = 3,355 - 5,994
C = -2,639 (which is not a valid number)
Continue the same process for the other combinations until we find a valid solution.