You received a $100 gift certificate to a clothing store. The store sells T-shirts for $14 and dress shirts for $21. You want to spend no more than the amount of the gift certificate. You want to leave at most $5 of the gift certificate unspent. You need at least one dress shirt. What are all of the possible combinations of T-shirts and dress shirts you could buy?
To find the possible combinations, we need to consider the constraints given:
1) We want to spend no more than the $100 gift certificate.
2) We want to leave at most $5 of the gift certificate unspent.
3) We need at least one dress shirt.
First, let's find the maximum number of dress shirts we can buy without exceeding the gift certificate amount:
$100 / $21 = 4 dress shirts (maximum)
Now, let's consider all the possible combinations:
1) 1 dress shirt + 0 T-shirts
Total cost = $21
Unspent gift certificate = $100 - $21 = $79 (greater than $5 unspent limit)
2) 2 dress shirts + 0 T-shirts
Total cost = 2 * $21 = $42
Unspent gift certificate = $100 - $42 = $58 (greater than $5 unspent limit)
3) 3 dress shirts + 0 T-shirts
Total cost = 3 * $21 = $63
Unspent gift certificate = $100 - $63 = $37 (less than $5 unspent limit)
4) 4 dress shirts + 0 T-shirts
Total cost = 4 * $21 = $84
Unspent gift certificate = $100 - $84 = $16 (less than $5 unspent limit)
5) 0 dress shirts + 1 T-shirt
Total cost = $14
Unspent gift certificate = $100 - $14 = $86 (greater than $5 unspent limit)
6) 1 dress shirt + 1 T-shirt
Total cost = $21 + $14 = $35
Unspent gift certificate = $100 - $35 = $65 (greater than $5 unspent limit)
7) 2 dress shirts + 1 T-shirt
Total cost = 2 * $21 + $14 = $56
Unspent gift certificate = $100 - $56 = $44 (greater than $5 unspent limit)
8) 3 dress shirts + 1 T-shirt
Total cost = 3 * $21 + $14 = $77
Unspent gift certificate = $100 - $77 = $23 (less than $5 unspent limit)
Note: We can't have more than 3 dress shirts as it exceeds the gift certificate amount.
Therefore, the possible combinations are:
1) 1 dress shirt + 0 T-shirts
2) 2 dress shirts + 0 T-shirts
5) 0 dress shirts + 1 T-shirt
6) 1 dress shirt + 1 T-shirt
7) 2 dress shirts + 1 T-shirt
8) 3 dress shirts + 1 T-shirt