Tom has a $20 bill, a $10 bill, a $5 bill, and $1 bill. List the total costs possible for items he could buy if he receives no change.

$20, $25, $30, $21, $10, $15, $11, $5, $6, $1

using 1 bill: 1, 5, 10, 20

using 2 bills 6, 11 ,21 15, 25, 30
using 3 bills : 16, 26, 31, 35
using 4 bills : 36
For a total of 15 different costs

Notice Madison missed a few

Or

the number of subsets of 4 things
= 2^4 = 16
but that includes the null set , or not using any bills
so our answer = 2^4 - 1 = 15

To find the possible total costs for items that Tom could buy without receiving any change, we can use a combination of the given bills. Let's go through the process step by step:

1. Start by listing the individual bills Tom has: $20, $10, $5, and $1.

2. Now, let's consider all possible combinations of these bills to form the total prices. We consider each bill individually and then combinations of two bills, three bills, and all four bills.

a. Individual bills:
- $20
- $10
- $5
- $1

b. Combinations of two bills:
- $20 + $10 = $30
- $20 + $5 = $25
- $20 + $1 = $21
- $10 + $5 = $15
- $10 + $1 = $11
- $5 + $1 = $6

c. Combinations of three bills:
- $20 + $10 + $5 = $35
- $20 + $10 + $1 = $31
- $20 + $5 + $1 = $26
- $10 + $5 + $1 = $16

d. Combinations of all four bills:
- $20 + $10 + $5 + $1 = $36

3. Now that we have listed all the possible combinations, we can compile the total costs Tom could buy without receiving any change:

- $20
- $10
- $5
- $1
- $30
- $25
- $21
- $15
- $11
- $6
- $35
- $31
- $26
- $16
- $36

Therefore, these are the total costs that Tom could buy if he receives no change: $20, $10, $5, $1, $30, $25, $21, $15, $11, $6, $35, $31, $26, $16, $36.