Answer:
(2 1/2, 10) and (3, 12).
Step-by-step explanation:
The variable x represents the number of pounds of sand. Mr. Weber needs at least 2 pounds of sand; this gives us the inequality
x ≥ 2
The center has only 6 lb of sand; this gives us the inequality
x ≤ 6, as he cannot buy more than they have.
The variable y represents the amount of gravel he buys. The center has only 13 lb of gravel in stock; this gives us the inequality
y ≤ 13, as he cannot buy more than they have.
Mr. Weber will buy at least twice as much gravel (y) as sand (x); this gives us the inequality
y ≥ 2x
The first ordered pair, (2 1/2, 10), fits the first inequality because 2 1/2 ≥ 2.
It fits the second inequality because 2 1/2 ≤ 6.
It fits the third inequality because 10 ≤ 13.
It fits the fourth inequality because 10 ≥ 2(2 1/2), or 10 ≥ 5.
The second ordered pair fits the first inequality because 3 ≥ 2. It fits the second inequality because 3 ≤ 6. It fits the third inequality because 12 ≤ 13. It fits the fourth inequality because 12 ≥ 2(3), or 12 ≥ 6.
The third ordered pair fits the first inequality because 4 ≥ 2. It fits the second inequality because 4 ≤ 6. It fits the third inequality because 6 ≤ 13. It does not, however, fit the last inequality because 6 is not greater than or equal to 2(4) or 8.
The fourth ordered pair fits the first ordered pair because 5 ≥ 2. It fits the second ordered pair because 5 ≤ 6. It fits the third inequality because
8 1/2 ≤ 13. It does not, however, fit the last inequality because 8 1/2 is not larger than 5(2) or 10.
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