alberto has 12 quarters, 10 dimes, 10 nickels, and 20 pennies. How many different combinations of coins can he make to have $2?
how many different way to make $2 useing 12 quaters,10 dimes,10 nickels, and 20 pennies
To find the number of different combinations of coins Alberto can make to have $2, we can use a systematic approach called combinations.
First, let's convert all of the coins into their respective dollar values:
- 12 quarters = 12 * $0.25 = $3
- 10 dimes = 10 * $0.10 = $1
- 10 nickels = 10 * $0.05 = $0.50
- 20 pennies = 20 * $0.01 = $0.20
Next, let's list out some possible combinations that can add up to $2 using these coins. Since quarters have the highest value, let's start with the maximum number of quarters we can use:
1) 3 quarters ($0.75) + 5 dimes ($0.50) + 5 nickels ($0.25) + 20 pennies ($0.20) = $2.70
We need to subtract the above combination because it exceeds $2. Let's continue listing the combinations and see which ones add up to exactly $2:
2) 2 quarters ($0.50) + 10 dimes ($1) + 5 nickels ($0.25) + 20 pennies ($0.20) = $1.95
3) 2 quarters ($0.50) + 5 dimes ($0.50) + 10 nickels ($0.50) + 20 pennies ($0.20) = $1.70
4) 1 quarter ($0.25) + 20 dimes ($2) + 2 nickels ($0.10) + 20 pennies ($0.20) = $2.55
5) 1 quarter ($0.25) + 15 dimes ($1.50) + 7 nickels ($0.35) + 20 pennies ($0.20) = $2.30
6) 1 quarter ($0.25) + 10 dimes ($1) + 12 nickels ($0.60) + 20 pennies ($0.20) = $2.05
7) 1 quarter ($0.25) + 5 dimes ($0.50) + 17 nickels ($0.85) + 20 pennies ($0.20) = $2.80
8) 1 quarter ($0.25) + 3 dimes ($0.30) + 20 nickels ($1) + 20 pennies ($0.20) = $2.75
9) 1 quarter ($0.25) + 1 dime ($0.10) + 23 nickels ($1.15) + 20 pennies ($0.20) = $2.70
10) 20 dimes ($2) + 10 nickels ($0.50) + 20 pennies ($0.20) = $2.70
11) 15 dimes ($1.50) + 15 nickels ($0.75) + 20 pennies ($0.20) = $2.45
12) 10 dimes ($1) + 20 nickels ($1) + 20 pennies ($0.20) = $2.20
13) 5 dimes ($0.50) + 25 nickels ($1.25) + 20 pennies ($0.20) = $1.95
14) 3 dimes ($0.30) + 30 nickels ($1.50) + 20 pennies ($0.20) = $1.80
15) 1 dime ($0.10) + 35 nickels ($1.75) + 20 pennies ($0.20) = $1.85
Therefore, there are 15 different combinations of coins that Alberto can make to have $2.