Solving One-Step Equations 2

Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to make a true equation where x has the greatest possible value.

Hint

How do the constants’ values affect the variable’s value?
Which constant should have a greater value?
Which constant should have a lesser value?

Answer

The greatest possible value of x is 85 when 12 + x = 97

Source: Robert Kaplinsky

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Greatest Common Factor

Directions: Using the digits 0 to 9 at most one time each, place a digit …

5 comments

  1. The greatest value of x is 85 when 12+x =97

  2. 85 + 12 = 97, x = 85

  3. Rudolf Österreicher

    Of the 173 unique ways to place the digits 1 to 9 at most one time each in each box to make a true equation (119 if you don’t allow leading zeros), x is greatest in the equation 12 + x = 97 (x = 85) or 04 + x = 91 / 05 + x = 92 / 06 + x = 93 if you allow the digit 0 and smallest in the equations
    35 + x = 47
    36 + x = 48
    37 + x = 49
    38 + x = 50
    46 + x = 58
    47 + x = 59
    48 + x = 60
    57 + x = 69
    58 + x = 70
    63 + x = 75
    73 + x = 85
    74 + x = 86
    78 + x = 90
    83 + x = 95
    84 + x = 96
    85 + x = 97

    or 39 + x = 41 if you allow zero

    • Rudolf Österreicher

      Correction: Without 0, there are 100 unique ways to place the digits 1 to 9 at most one time each in each box to make a true equation (times 4 because you could swap the addends, swap the tenths digits of the addends or swap the unit digits of the addends). With 0, there are 173 ways and with non-leading zeros there are 119 ways.

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