3.08: Constraints 1. Jacob is ordering custom T-shirts for his soccer team. Long

Question

3.08: Constraints

1. Jacob is ordering custom T-shirts for his soccer team. Long-sleeved shirts cost $15 each and short-sleeved shirts cost $10 each. Jacob can spend at most $250 and he wants to order at least 20 shirts.

Let x represent the number of long-sleeved shirts. Let y represent the number of short-sleeved shirts.

Which inequalities are among the constraints for this situation?

Select each correct answer.

15x+10y250

x+y20

15x+10y20

15x+10y250

x+y250

x+y20

2.Alia needs to bring at least 25 pieces of fruit to a training practice. She suggested apples and oranges and was told to be sure to bring more than 10 apples.

Let x represent the number of apples and y represent the number of oranges.

Which inequalities model the situation?

Select each correct answer.

x+y>25

x10

x>10

y0

x+y25

3. The triangular region shows the number of possible ounces of pepperoni slices, x, and the number of possible ham slices, y, a pizza maker can use on a special pizza.

Which combination of pepperoni and ham can the pizza maker use?

38 pepperoni slices and 30 ham slices

33 pepperoni slices and 15 ham slices

43 pepperoni slices and 25 ham slices

25 pepperoni slices and 20 ham slices

4. Mr. Chen goes to the post office to buy small and large boxes. He needs at least 4 small boxes. Altogether, he will buy no more than 15 boxes. The post office has 10 small boxes and 9 large boxes in stock.

The graph shows the feasible region, where x represents the number of small boxes and y represents the number of large boxes.

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

Select each correct answer.

(6,9)

(7,10)

(8,6)

(9,8)

5. Gillian can spend up to $300 buying both cotton shirts and wool shirts for her club. The cotton shirts cost $15 each and the wool shirts cost $20 each. The number of wool shirts Gillian will buy will be at least 3, and no more than half the number of cotton shirts she buys.

The graph shows the feasible region, where x represents the number of cotton shirts and y represents the number of wool shirts.

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

Select each correct answer.

(12,5)

(13,4)

(16,4)

(11,4)

(6,2)

Explanation / Answer

Price for x long sleeved shirts will be 15x

Price for y short sleeved shirts will be 10y

Jacob can spend at most $250

Therefore the equations will be

x+y20

15x+10y250

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