Eight U.S. coins are worth a total of 38 cents. How many of the coins are dimes?
To find the number of dimes among eight U.S. coins worth a total of 38 cents, we can use a bit of algebra. Let's set up the problem:
Let x be the number of dimes.
Since we have a total of eight coins, the remaining coins must be nickels (8 - x nickels).
The value of x dimes is 10x cents.
The value of (8 - x) nickels is 5(8 - x) cents.
According to the problem, the total value is 38 cents. So, we can write the equation:
10x + 5(8 - x) = 38
Now, let's solve this equation step by step:
10x + 40 - 5x = 38
Combining like terms:
5x + 40 = 38
Subtract 40 from both sides:
5x = 38 - 40
5x = -2
Divide by 5:
x = -2/5
We have a problem here. The solution is not a whole number, which doesn't make sense in this context. Therefore, there must have been an error in the information provided or in the setup of the problem.
Please double-check the question or verify if there was any particular condition imposed on the coins.
make a list of possible coins to give you 38 cents
e.g.
Q D N P
1 1 0 3
1 0 2 3
...
0 0 7 3
...
then pick the one where the sum of coins is 8