Luis can spend up to $240 buying men’s and women’s shirts for his club. men’s shirts cost $8 each and women’s shirts cost $12 each. he needs to buy at least 3 of each type of shirt. also, the women’s shirts must be at least twice the number of men’s shirts. which combinations of men’s and women’s shirts can luis buy? select each correct answer.

7 men’s shirts and 17 women’s shirts

6 men’s shirts and 15 women’s shirts

5 men’s shirts and 8 women’s shirts

4 men’s shirts and 9 women’s shirts

The correct options are 2 and 4.

Step-by-step explanation:

Let x be the number o men's shirts and y be the number of women's shirts.

Cost of men’s shirts = $8

Cost of women’s shirts = $12

Luis can spend up to $240 buying men’s and women’s shirts for his club.

               ..... (1)

He needs to buy at least 3 of each type of shirt.

              .... (2)

The women’s shirts must be at least twice the number of men’s shirts.

               .... (3)

Check all the given options whether they satisfy all the above inequalities or not.

In option 1, (7,17).

This statement is false. Therefore (7,17) is not a possible solution.

In option 2, (6,15).

This statement is true.

This statement is true.

This statement is also true. Therefore (6,15) is a possible solution.

In option 3, (5,8)

Check this point for inequality (3).

This statement is false. Therefore (5,8) is not a possible solution.

In option 4, (4,9).

This statement is true.

This statement is true.

This statement is also true. Therefore (4,9) is a possible solution.

From the below graph it is clear that the points (6,15) and (4,9) lie on the feasible region.

Therefore, the correct options are 2 and 4.

answer:   (s+1)(s+4)

step-by-step explanation:

factor s2+5s+4

s2+5s+4

=(s+1)(s+4)