In two inequalities below,both a and b are integers.how many values do a and b have in common?
4< a < 21 12< b < 24
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a can be 5, 6, .. 19 or 20
b can be 13, 14, ...22 or 23.
Both a or b can be integers 13 through 20. Those are the "values in common" to both sets.
To find the common values between the two sets of inequalities, we need to determine the overlapping range for both "a" and "b".
The first inequality states that "a" is between 4 and 21, exclusive, so the possible values for "a" are 5, 6, 7, ..., 19, or 20. This set includes 16 values.
The second inequality states that "b" is between 12 and 24, exclusive, so the possible values for "b" are 13, 14, 15, ..., 22, or 23. This set includes 11 values.
To find the values that both sets have in common, we need to identify the overlapping range between the minimum and maximum values for both "a" and "b". In this case, the overlapping range is from 13 to 20, inclusive.
Therefore, both "a" and "b" have 8 common values: 13, 14, 15, 16, 17, 18, 19, and 20.