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−_ _._=_ _._
x - 16.9 = 60.8
To check that the solution is correct, we can solve for x:
x = 60.8 + 16.9
x = 77.7
Our solution is correct because we used all digits 1-9 exactly once and the equation gives the desired solution x = 77.7.
To solve for x=77.7 using the digits 1-9 only once, let's break down the equation step-by-step:
Step 1: We know that x−_ _._=_ _._
Based on x=77.7, we can conclude that the first digit after the decimal point in the missing numbers should be 7.
Step 2: Now the equation becomes x−_ 7._=_ _._
We still need to determine the second digit after the decimal point in the missing numbers.
Step 3: Since we need to add up to 77, we want the first digit before the decimal point to be as small as possible, so we choose 1.
Step 4: The equation becomes 1 7._=60._
To reach a sum of 77, the smallest number we can use for the second digit before the decimal point is 6.
Step 5: The equation now becomes 1 7.6 = 60.1
By filling in the blanks, the equation becomes x−16.7=60.1, which simplifies to x=77.7. Therefore, we have determined the correct equation to solve for x=77.7.
To create an equation where the solution is x = 77.7, we can use the digits 1-9 to fill in the blanks in the equation x− _ _._ = _ _._.
Step 1: We need to determine the integer part of the solution. Since x is the integer part, it should be a whole number from 1 to 9. Taking into account that x− _ _._ should be greater than or equal to 77, and 77.7 is closer to 78, we can deduce that x should be 8.
Step 2: We need to determine the decimal part of the solution. Since we have already assigned 8 to the integer part, we only have the digits 1-9 remaining for the decimal part. To achieve 77.7, we can place 7 as the first digit after the decimal point.
Thus, the equation becomes:
x− 7._ = 7._
Step 3: Now, we need to find a number that, when subtracted by 7.0, leaves a decimal part of 0.7. To get 0.7, we can add 7 to the initial decimal part, resulting in 7.7.
Therefore, the final equation is:
8− 7.7 = 7.7
When we subtract 7.7 from 8, we indeed get 0.3, which indicates that our answer is correct. Thus, x = 77.7 is the solution to the equation x−_ _._=_ _._.