Question 1058559: The sum of the atomic number of two elements is not more than 22, with an average 11 and with a difference less than 16. What are the possible atomic numbers?
Answer by solve_for_x(190)   (Show Source):
You can put this solution on YOUR website! Let x represent one atomic number, and let y represent the other.
Since the sum is not more than 22, you can write:
x + y ≤ 22
Since the average is equal to 11, you can write:
(x + y)/2 = 11
which can be rearranged as:
x + y = 2(11)
x + y = 22
Thus, the sum is not only "not more than 22", is must be exactly 22.
Then, since the difference is less than 16, you can write:
x - y < 16
Solving x + y = 22 for y gives:
y = 22 - x
Substituting that into the inequality gives:
x - (22 - x) < 16
x - 22 + x < 16
2x - 22 < 16
2x < 16 + 22
2x < 38
x < 19
Then, solving x + y = 22 for x gives:
x = 22 - y
Substituting this into inequality gives:
22 - y - y < 16
22 - 2y < 16
-2y < 16 - 22
-2y < -6
y > 3 (remember to reverse the inequality sign when multiplying or dividing by a negative number)
Thus, the combinations must have x < 19 and y > 3
The set of combinations is then:
(4, 18), (5, 17), (6, 16), (7, 15), (8, 14), (9, 13), (10, 12), and (11, 11)
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