Question

Kiani is shopping at a bookstore with a budget of $60. Hardbacks cost $12 and paperbacks cost $5. Write a two-variable inequality and determine the constraints of the problem. Which of the following points represents a viable solution?(1 point)
Responses

(6,6)

(−2,6)

(1,4.5)

(2,4)

Answer 1

you can only choose one

Answer 2

This graph shows the inequality 25x+15y≥200 , and represents Lina’s earnings for lawn mowing and dog walking where x represents the number of lawns mowed and y represents the number of dogs walked. Which of the labeled points is a viable solution in this context?

(1 point)
Responses

None of the points are a viable solution.

(2,3)

(10,10)

(20,11.5)

Answer 3

Let x be the number of hardbacks and y be the number of paperbacks that Kiani purchases.

The two-variable inequality for the budget constraint is:

12x + 5y ≤ 60

The constraints are:

x ≥ 0 (non-negative number of hardbacks)
y ≥ 0 (non-negative number of paperbacks)

Now, we substitute the given points into the inequality to determine which one represents a viable solution.

1) (6,6):
12(6) + 5(6) = 72 + 30 = 102 > 60
This point does not satisfy the inequality, so it is not a viable solution.

2) (-2,6):
12(-2) + 5(6) = -24 + 30 = 6 ≤ 60
This point satisfies the inequality and the constraints. It represents a viable solution.

3) (1,4.5):
12(1) + 5(4.5) = 12 + 22.5 = 34.5 ≤ 60
This point satisfies the inequality and the constraints. It represents a viable solution.

4) (2,4):
12(2) + 5(4) = 24 + 20 = 44 ≤ 60
This point satisfies the inequality and the constraints. It represents a viable solution.

Therefore, the points (−2,6), (1,4.5), and (2,4) all represent viable solutions.

Answer 4

Apologies for the confusion. In that case, the point that represents a viable solution is (2,4).

Answer 5

To determine which of the labeled points is a viable solution, we substitute the x and y values into the inequality 25x + 15y ≥ 200.

1) (2,3):
25(2) + 15(3) = 50 + 45 = 95 < 200
This point does not satisfy the inequality and is not a viable solution.

2) (10,10):
25(10) + 15(10) = 250 + 150 = 400 ≥ 200
This point satisfies the inequality and is a viable solution.

3) (20,11.5):
25(20) + 15(11.5) = 500 + 172.5 = 672.5 ≥ 200
This point satisfies the inequality and is a viable solution.

Therefore, the viable solution is (10,10).