Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create an equation where x has the greatest possible value.
Hint
How does the value of the number being added to x affect the value of x?
How does the value of the sum affect the value of x?
How can we tell whether it is better for the two missing numbers to have a larger or smaller value?
How does the value of the sum affect the value of x?
How can we tell whether it is better for the two missing numbers to have a larger or smaller value?
Answer
The equation 12 + x = 98 results in x having a value of 86.
Source: Robert Kaplinsky
If you would like the value of x to be included in the “no repeated numbers”, the equation would be 12 + x = 97 and x = 85
Ooh. Neat modification.
Talking with some colleagues, we are thinking that this problem may fall better under 6.EE.6. Good problem either way.
X cannot be greater than 9 right? If so than:
1 x 3 + x = 2 x 6
3 + x = 12
x = 9
9 is the biggest possible number.
there is no restriction on x. The boxes can only contain numbers between 0-9.
This is an addition problem
12+X=98
-12 -12
X=86
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Adding onto that: The smallest possible value for x is 2 in the equations
29+x=31
39+x=41
49+x=51
59+x=61
69+x=71
79+x=81