Question

Mr. Weber drives to a landscape supply center to buy sand and gravel. He needs at least 2 lb of sand. The amount of gravel he will buy will be at least twice the amount of sand he will buy. The center has 6 lb of sand and 13 lb of gravel in stock.
The graph shows the feasible region, where x represents the number of pounds of sand and y represents the number of pounds of gravel.

Which ordered pairs meet all the constraints and make sense in the context of the situation?

Select each correct answer.



(2 1/2, 10)

(3, 12)

(4,6)

(5, 8 1/2)

Answer 1

The answers are (2 1/2, 10) and (3, 12)

//I just took the test and these were the answers

Answer 2

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.