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?
To find all the possible combinations of T-shirts and dress shirts that could be bought using the gift certificate, we need to consider the constraints given:
1. The cost of a T-shirt is $19 and the cost of a dress shirt is $27.
2. The total cost of the items purchased should not exceed $150.
3. The remaining amount should be at most $9.
Since we want to buy at least two dress shirts, let's consider the maximum number of dress shirts we can purchase:
Maximum dress shirts = (Maximum allowable cost − Cost of T-shirts) ÷ Cost of a dress shirt
Maximum dress shirts = (150 - 2×19) ÷ 27
Maximum dress shirts = 112 ÷ 27
Maximum dress shirts ≈ 4
Therefore, we can buy at most 4 dress shirts. Now, let's consider different combinations of dress shirts and T-shirts to see which options meet all the given constraints.
1. 4 dress shirts: Cost = 4 × 27 = $108
Remaining amount = 150 - 108 = $42
This leaves enough room to buy at least two T-shirts:
Possible combinations:
- 2 T-shirts: Cost = 2 × 19 = $38
- 3 T-shirts: Cost = 3 × 19 = $57
- 4 T-shirts: Cost = 4 × 19 = $76
2. 3 dress shirts: Cost = 3 × 27 = $81
Remaining amount = 150 - 81 = $69
This leaves enough room to buy at least three T-shirts:
Possible combinations:
- 3 T-shirts: Cost = 3 × 19 = $57
No other combinations of dress shirts provide enough remaining amount to buy additional T-shirts. Thus, the possible combinations are:
- 4 dress shirts and 2 T-shirts
- 4 dress shirts and 3 T-shirts
- 4 dress shirts and 4 T-shirts
- 3 dress shirts and 3 T-shirts