_ _
x _
_____
_ _
+_ _
______
_ _
You can only use numbers 1-9 and each can be used once.
To solve this equation, we need to find the values of the variables represented by the underscores (_).
Let's break down the given equation into three separate parts:
1. The top line: _ _ x _ = _ _ (Let's call this equation A)
2. The middle line: _ _ + _ _ = _ _ (Let's call this equation B)
3. The bottom line: _ _ - _ _ = _ _ (Let's call this equation C)
Now, let's solve these equations one by one:
Equation A:
Based on the given constraints, we can start by examining the possibilities for the first two digits.
Since we need to multiply a two-digit number (represented by _ _) by a one-digit number, the maximum value for the first digit can be 9 (since we're only allowed to use numbers 1-9).
The maximum value for the second digit would then be 8 (since it cannot be the same as the first digit).
So, we have the equation:
9 _ x 8 = _ _
From here, we need to find two digits that, when multiplied together, give us a two-digit product. A quick assessment reveals that the only combination satisfying this requirement is 92 x 8 = 736.
Therefore, we have:
9 2 x 8 = 7 3 6
Now let's move on to Equation B:
Equation B:
Similarly, we can determine the range of possible values for the first two digits of the middle line.
Using numbers 1-9 and being mindful of not using the digits already used in Equation A, we find that the maximum value for the first digit can be 7 (since we already used 8).
The maximum value for the second digit would then be 6 (since it cannot be the same as the first digit).
So, we have the equation:
7 _ + 6 _ = _ _
To find the values that satisfy this equation, we need to find two digits that, when added together, give us a two-digit sum.
The only combination satisfying this requirement is 7 + 6 = 13.
Therefore, we have:
7 1 + 6 3 = 8 4
Finally, let's move on to Equation C:
Equation C:
Since we need to subtract a two-digit number (represented by _ _) from a one-digit number, the maximum value for the first digit can be 8 (keeping in mind digits used in Equation A and Equation B).
The maximum value for the second digit would then be 4 (since it cannot be the same as the first digit).
So, we have the equation:
8 _ - 4 _ = _ _
To find the values satisfying this equation, we need to find two digits that, when subtracted, give us a two-digit difference.
The only combination satisfying this requirement is 8 - 4 = 4.
Therefore, we have:
8 4 - 4 0 = 4 4
Now, we have found the values for all the variables represented by the underscores in the equation:
_ _ x _ = _ _ → 9 2 x 8 = 7 3 6
_ _ + _ _ = _ _ → 7 1 + 6 3 = 8 4
_ _ - _ _ = _ _ → 8 4 - 4 0 = 4 4