Using the digits 1–9, at most one time each, fill in the blanks to make an equation where the solution is x=77.7. Explain how you know you are correct.
x−_ _._=_ _._
AAAaannndd the bot gets it wrong yet again!
sorry - you used 6 twice
To make an equation where the solution is x = 77.7, we need to fill in the blanks with appropriate digits. Let's break down the equation step by step.
x - _ _ . _ = _ _ . _
To get the decimal point in the correct position, we need to choose a digit to occupy the empty hundredth's place. We can select any digit from 1 to 9 since we can use each digit only once. Let's choose 7 for the hundredth's place.
x - _ _ . _ = 7_ . _
Now, we need to choose a digit for the tenth's place. Since we want x to be equal to 77.7, the tenth's digit should be 7.
x - _ _ . _ = 77 . _
Finally, for the unit's place, we can choose any remaining digit from 1 to 9. Again, let's choose 7.
x - _ _ . _ = 77 . 7
Now, our equation becomes:
x - 7 _ . _ = 77 . 7
To find out the missing digit in the hundredth's place, we can subtract 7 from both sides of the equation:
x - 7 - 7 _ . _ = 77 . 7 - 7
Simplifying the equation:
x - 14 _ . _ = 70 . 7
Now, to isolate x, we add 14 to both sides of the equation:
x - 14 + 14 _ . _ = 70 . 7 + 14
Simplifying further:
x _ . _ = 84 . 7
We have filled in the blanks correctly, and the equation becomes:
x - 7 7 . 7 = 77 . 7
Therefore, the solution is x = 77.7, and we know we are correct because we have followed the steps to create an equation that results in the desired value of x.
To solve this, we need to fill in the blanks with appropriate digits to make the equation x−_ _._=_ _._, where x equals 77.7.
Let's break it down step by step:
1. The integer part of x is 77. So, we can fill in the first blank with the digit 7: x−7_._=_ _._.
2. Now, we need to place a decimal point. For the fractional part, we want 7 tenths. Since we have already used the digit 7, we cannot use it again. So, we need to use the digit 1: x−7.1=_ _._.
3. The remaining digits are 2, 3, 4, 5, 6, 8, and 9. We need to fill in the last blank with a combination of these digits to make the fractional part 7 hundredths. Among the remaining digits, the only pair that adds up to 7 is 3 and 4. So, we can fill in the last blank as follows: x−7.1=3_._.
4. Finally, we fill in the last remaining blank with the only available digit, which is 4: x−7.1=34..
The completed equation is x−7.1=34, which simplifies to x = 77.7.
To confirm that our solution is correct, we substitute the value of x back into the equation. If the equation holds true, then our solution is correct.
x−7.1=34
77.7−7.1=34
70.6=34
This is not a true statement, so we made an error somewhere in our initial steps. We need to go back and find the mistake to rectify it.
x−9.6=68.1
To find the missing digits, we subtract 9.6 from both sides:
x−9.6=68.1
+9.6 +9.6
x=77.7
We know this is correct because when we substitute 77.7 back into the equation, we get:
77.7−9.6=68.1
68.1 = 68.1
Which is true. Therefore, x=77.7 satisfies the equation.