you have 95 coins that total $10.75. the coins consist of only quarters and nickels. how many of each coin do you have?
.25q+.05n=10.75 (1)
q+n=95 (2)
Multiply (2) by -.25 to cancel the q's
.25q+.05n=10.75 (1)
-.25q-.25n=-23.75 (3)
-.2n=-13
Divide both sides by -.2
n=65
From (2), q+n=95, q+65=95, q=30
When plugged back into equation 1, it checks. It works in both equations, so this is your solution.
You have a total of $175 in $5 and $20 bills. The number of $5 bills you have is 3 more than 4 times the number of $20 bills. How many of each type of bill do you have?
To solve this problem, let's assign variables to represent the number of quarters and nickels. Let:
Q = number of quarters
N = number of nickels
Given that you have a total of 95 coins, we can write the equation Q + N = 95.
Additionally, we know that the total value of the coins is $10.75. Since a quarter is worth $0.25 and a nickel is worth $0.05, we have the equation 0.25Q + 0.05N = 10.75.
Now, we have a system of two equations:
Q + N = 95
0.25Q + 0.05N = 10.75
To solve this system, we can use the method of substitution. Rearrange the first equation to solve for N:
N = 95 - Q
Substitute this value of N into the second equation:
0.25Q + 0.05(95 - Q) = 10.75
Simplify the equation:
0.25Q + 4.75 - 0.05Q = 10.75
0.20Q = 6
Q = 6 / 0.20
Q = 30
Now substitute the value of Q back into the first equation to solve for N:
30 + N = 95
N = 95 - 30
N = 65
So, you have 30 quarters and 65 nickels.
To solve this problem, we can set up a system of equations to represent the given information.
Let's assume the number of quarters as Q, and the number of nickels as N.
From the problem statement, we know two key pieces of information:
1. The total number of coins is 95. So, the first equation is:
Q + N = 95
2. The total value of the coins is $10.75, where each quarter contributes 25 cents and each nickel contributes 5 cents. So, the second equation is:
25Q + 5N = 1075 (since 1 dollar = 100 cents)
Now, we have a system of equations:
Q + N = 95
25Q + 5N = 1075
To solve this system, we can use either substitution or elimination methods. Let's use the elimination method in this case.
Multiply the first equation by 5 to make the coefficients of N match:
5Q + 5N = 475
Now, subtract this equation from the second equation to eliminate N:
25Q + 5N - (5Q + 5N) = 1075 - 475
20Q = 600
Solving for Q:
Q = 600 / 20
Q = 30
Substitute the value of Q back into the first equation to find N:
30 + N = 95
N = 95 - 30
N = 65
So, there are 30 quarters and 65 nickels.
To check if our answer is correct, we can verify if the total number of coins is 95 and the total value of the coins is $10.75.
Number of coins: 30 (quarters) + 65 (nickels) = 95 (matches the given total)
Value of the coins: (30 quarters * 25 cents) + (65 nickels * 5 cents) = 750 cents + 325 cents = 1075 cents = $10.75 (matches the given total)
Therefore, our answer is correct, and we have 30 quarters and 65 nickels.