how many quarters nickels and dimes are in $45 quarters 5 times more than nickels, and nickels 3 times more than the dimes
25q+5n+10d = 4500
q = 5n
n = 3d
So, start substituting and the values will become clear.
Let's solve the problem step by step.
Let's assume the number of dimes as "x".
1. Quarters: We are given that the total value of quarters is $45. Since 4 quarters make $1, the number of quarters would be 45 *4 = 180.
2. Nickels: We are given that nickels are 3 times more than dimes. So, the number of nickels would be 3x.
3. Dimes: We already assumed the number of dimes as "x".
Now, since we know that 5 nickels make $0.25 (equivalent to 1 quarter), we can calculate the number of nickels as follows:
Number of nickels = 180 * 5 = 900
And since nickels are 3 times more than dimes, we can calculate the number of dimes as follows:
Number of dimes = 900 / 3 = 300
So, the final answer is:
- Quarters: 180
- Nickels: 900
- Dimes: 300
To find out how many quarters, nickels, and dimes are in $45, we can set up a system of equations based on the given information.
Let's assume the number of dimes as 'x'.
Since nickels are said to be 3 times more than the dimes, the number of nickels would be 3x.
Similarly, since quarters are said to be 5 times more than the number of nickels, the number of quarters would be 5(3x) = 15x.
Now, let's calculate the value of the coins in dollars:
The value of dimes in dollars = x * $0.10 = $0.10x
The value of nickels in dollars = (3x) * $0.05 = $0.15x
The value of quarters in dollars = (15x) * $0.25 = $3.75x
According to the problem, the sum of the values of the coins equals $45:
$0.10x + $0.15x + $3.75x = $45
Combining like terms, we have:
$3.85x = $45
Dividing both sides by $3.85, we find:
x = $45 / $3.85
x ≈ 11.69
Since we can't have a fraction of a coin, we round down to the nearest whole number. Therefore, the number of dimes is 11.
Now that we know the number of dimes, we can find the number of nickels and quarters:
Number of nickels = 3x = 3 * 11 = 33
Number of quarters = 15x = 15 * 11 = 165
So, there are 165 quarters, 33 nickels, and 11 dimes in $45.