a purse contains $1.35 in quarters nickels and dimes There are 3 times as many dimes as quarters and 3 more nickels than quarters. find the number of each coin
I need the answer.
To find the number of each coin, we can set up a system of equations based on the given information.
Let's represent the number of quarters as Q, the number of dimes as D, and the number of nickels as N.
We know that there are 3 times as many dimes as quarters, so we can write the equation:
D = 3Q
We also know that there are 3 more nickels than quarters, so:
N = Q + 3
Now, let's calculate the value of the coins in cents:
The value of quarters in cents = 25Q
The value of dimes in cents = 10D
The value of nickels in cents = 5N
Since the total value of the coins in the purse is $1.35, we can write the equation:
25Q + 10D + 5N = 135
Now we have a system of equations:
D = 3Q
N = Q + 3
25Q + 10D + 5N = 135
To solve this system of equations, we can substitute the values of D and N from the first two equations into the third equation.
Substituting D = 3Q and N = Q + 3 into the equation 25Q + 10D + 5N = 135, we get:
25Q + 10(3Q) + 5(Q + 3) = 135
25Q + 30Q + 5Q + 15 = 135
60Q + 15 = 135
60Q = 135 - 15
60Q = 120
Q = 120/60
Q = 2
Now that we know the value of Q, we can substitute it back into the other equations to find the values of D and N.
D = 3Q = 3(2) = 6
N = Q + 3 = 2 + 3 = 5
Therefore, there are 2 quarters, 6 dimes, and 5 nickels in the purse.