Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create an equation such that the solution is the largest integer possible.
Hint
How might a backwards approach be able to support you? What is an integer?
Answer
There are many correct answers.
Potential Answer: (9/3)x+1=(4/2)x+8; x = 7
Potential Answer: (4/2)x+1=(9/3)x+8; x = -7
Potential Answer: (9/3)x+1=(4/2)x+8; x = 7
Potential Answer: (4/2)x+1=(9/3)x+8; x = -7
Source: Kristen Amaral
One of my students came up with:
3/4 x + 1 = 5/8 x + 9
x=64
Prompt says largest integer possible, so isn’t there only one solution?
If you can only use each number 1 time the solution you posted has a 4 used twice (3/4 and 64).
You don’t have to worry about the solution repeating numbers you used in the equation.
We got x=120 with 1/5x+9=2/8x+3
Credit to student in grade 8:
(5/9)x +8 = (4/7)x +1
x=441