There are 6 times as many dimes as quarters, and 6 times more nickels than quarters. If you have $5.70, how much money do you have in quarters?
X Qtrs.
6X Dimes.
(X+6) Nickels.
25*x + 10*6X + 5*(X+6) = 570.
25x + 60x + 5x+30 = 570
90x = 570-30 = 540
X = 6 Quarters.
Amount = 6 * $.25 = $1.50.
To solve this problem, we'll use a system of equations. Let's start by assigning variables to the unknown quantities.
Let's say:
Q = number of quarters
D = number of dimes
N = number of nickels
We are given two pieces of information:
1. "There are 6 times as many dimes as quarters": D = 6Q
2. "6 times more nickels than quarters": N = 6Q
Now let's calculate the value of these coins in terms of cents since it is easier to work with than dollars.
The value of a quarter is 25 cents. So the total value of quarters is 25Q cents.
The value of a dime is 10 cents. So the total value of dimes is 10D cents.
The value of a nickel is 5 cents. So the total value of nickels is 5N cents.
We are also given that the total value of all the coins is $5.70, which is equal to 570 cents. Thus, we can write the equation:
25Q + 10D + 5N = 570
Now let's substitute the expressions for D and N in terms of Q into this equation:
25Q + 10(6Q) + 5(6Q) = 570
25Q + 60Q + 30Q = 570
115Q = 570
Now we can solve for Q by dividing both sides of the equation by 115:
Q = 570/115
Q ≈ 4.96
Since the number of quarters must be a whole number (you can't have a fraction of a quarter), we round Q down to the nearest whole number:
Q = 4
Therefore, you have 4 quarters. Since each quarter is worth 25 cents, the total value of the quarters is:
4 x 25 = 100 cents
In other words, you have $1.00 in quarters.