Tanya had $1.19 in coins. None of the coins were dollars or 50-cent pieces. Josie asked Tanya for change for a dollar, but she did not have the correct change. Which coins did Tanya have
3 quarters, 4 dimes and 4 pennies.
.75+.40+.04=1.19
To determine which coins Tanya had, let's break down the problem step by step:
1. We know that Tanya had $1.19 in coins and that none of the coins were dollars or 50-cent pieces.
2. Let's assume Tanya only had coins in denominations smaller than 50 cents.
3. We also know that Josie asked Tanya for change for a dollar and that Tanya did not have the correct change.
4. If Tanya had only 25-cent pieces, she would need five of them to make a dollar. However, this would leave her with only 19 cents remaining, which cannot be made up using only smaller coins.
5. If Tanya had only 10-cent pieces, she would need ten of them to make a dollar. This would leave her with only nine cents remaining, which also cannot be made up using only smaller coins.
6. If Tanya had only 5-cent pieces, she would need twenty of them to make a dollar. This would leave her with only nineteen cents remaining, which fits with the given amount.
Therefore, Tanya had nineteen 5-cent pieces (nickels).
So, Tanya had 19 nickels.
To find out which coins Tanya had, we can try a process of elimination.
Let's start by assuming Tanya had one of each coin: a penny, a nickel, a dime, and a quarter.
The total value of these coins would be 1 cent (penny) + 5 cents (nickel) + 10 cents (dime) + 25 cents (quarter) = 41 cents. However, this total is less than the given amount of $1.19.
So, we need to adjust our assumption by removing one of the coins and trying again.
If we remove the penny, the new total would be 5 cents (nickel) + 10 cents (dime) + 25 cents (quarter) = 40 cents.
This is still less than $1.19, so let's remove another coin.
If we remove the nickel, the new total would be 10 cents (dime) + 25 cents (quarter) = 35 cents.
Again, still less than $1.19, so let's remove the next coin.
If we remove the dime, the new total would be 25 cents (quarter) = 25 cents.
This is still less than $1.19, so let's remove the last coin.
If we remove the quarter, the new total would be 0 cents.
Since this is less than the given amount of $1.19, we can conclude that Tanya did not have one of each coin.
Now, considering the remaining possibilities, Tanya must have had a dime, a nickel, and some pennies.
Let's calculate the remaining amount by finding the difference between $1.19 and the value of a dime and a nickel:
$1.19 - 10 cents (dime) - 5 cents (nickel) = $1.19 - 15 cents = $1.04.
Since none of the remaining coins can be dollars or 50-cent pieces, the only possible coins Tanya had are pennies.
To see how many pennies Tanya had, divide the remaining amount, $1.04, by the value of a penny:
$1.04 รท 1 cent (penny) = 104 pennies.
Therefore, Tanya had a dime, a nickel, and 104 pennies.