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−_ _._=_ _._
(2 points)
AAAaannndd the bot gets it wrong yet again!
sorry - you used 3 and 4 more than once.
whats the right answer then
To solve this problem, we need to find the missing digits that will make the equation x - _ _ . _ = _ _ . _ equal to x = 77.7.
Since the solution is x = 77.7, we know that the second digit after the decimal point in x needs to be 7.
Now, let's focus on the left-hand side of the equation, x - _ _ . _ . Since we can only use the digits 1-9 at most one time each, we need to find a combination of digits that will subtract from x and result in 70.
One possible combination is 99. Since 99 subtracted from any two-digit number will result in a number ending with 1 (e.g., 77 - 99 = -22), this means we can use 99 as the second and third digits after the decimal point on the left-hand side of the equation:
x - 99._ = _ _ . 7
Now, we need to find the first digit after the decimal point on the left-hand side of the equation. We know that x needs to be a two-digit number, so the first digit after the decimal point needs to be 7.
Thus, the equation becomes:
x - 99._ = 7 _ . 7
Now, we need to find the remaining digit to complete the equation. We know that adding 99._ to 77._ will result in 7 _ . 7, so the missing digit would be 7 as well.
Therefore, the equation to make x = 77.7 and satisfy the given conditions is:
x - 99.7 = 77.7
To verify whether this equation is correct, we can substitute it back into the original equation:
77.7 - 99.7 = 77.7
-22 = 77.7
Since -22 does not equal 77.7, we can conclude that this equation is incorrect.
Hence, we cannot find a correct equation using the digits 1–9 at most one time each to make x = 77.7.
One possible equation using the given digits is:
x – 23.4 = 54.3
If we add 23.4 to both sides, we get:
x = 77.7
So, the solution to this equation is x = 77.7.
I know I am correct because I followed the order of operations, and the equation I came up with produces the desired result.