You received a $150 gift certificate to a clothing store. The store sells T-shirts for $19 and dress shirts for $27. You want to spend no more than the amount of the gift certificate. you want to leave at most $9 of the gift certificate unspent. You need at least two dress shirts. What are all of the possible combinations of T-shirts and dress shirts you could buy?

Question

You received a ​$150 gift certificate to a clothing store. The store sells​ T-shirts for ​$19 and dress shirts for ​$27. You want to spend no more than the amount of the gift certificate. you want to leave at most ​$9 of the gift certificate unspent. You need at least two  dress shirts. What are all of the possible combinations of​ T-shirts and dress shirts you could​ buy?

Select all that apply.

A.)two ​T-shirts and four dress shirts
B.) one​T-shirts and four  dress shirts.
C.)three ​T- shirts and three dress shirts.
 D.)No ​T- shirts and five dress shirts.

GPT 3.5 · Answer

To find all the possible combinations of T-shirts and dress shirts that fit the given criteria, we can set up an inequality equation.

Let x be the number of T-shirts and y be the number of dress shirts.

The cost of x T-shirts is 19x dollars.
The cost of y dress shirts is 27y dollars.

We want to spend no more than the amount of the gift certificate, which is $150. We also want to leave at most $9 of the gift certificate unspent.

Therefore, the inequality equation is:

19x + 27y ≤ 150 + 9

Simplifying the equation, we get:

19x + 27y ≤ 159

To find all the possible combinations of T-shirts and dress shirts, we can try different values of x and y that satisfy the inequality.

Now, let's try the options:

A.) two T-shirts and four dress shirts:
19(2) + 27(4) = 38 + 108 = 146 (less than or equal to 159)
This combination satisfies the inequality.

B.) one T-shirt and four dress shirts:
19(1) + 27(4) = 19 + 108 = 127 (less than or equal to 159)
This combination satisfies the inequality.

C.) three T-shirts and three dress shirts:
19(3) + 27(3) = 57 + 81 = 138 (less than or equal to 159)
This combination satisfies the inequality.

D.) No T-shirts and five dress shirts:
19(0) + 27(5) = 0 + 135 = 135 (less than or equal to 159)
This combination satisfies the inequality.

Therefore, all of the possible combinations of T-shirts and dress shirts that fit the given criteria are:

A.) two T-shirts and four dress shirts.
B.) one T-shirt and four dress shirts.
C.) three T-shirts and three dress shirts.
D.) No T-shirts and five dress shirts.

So, all options apply.