Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 31 coins with a total face value of $4.55, how many of the coins are nickels?
q = # of quarters
n = # of nickels
q + n = 31 coins
Now, you need the value of the coins:
.25q + .05n =4.55
I would multiply by 100 to get rid of the decimals
25q + 5n = 455
q + n + 31
(multiply this equation by negative 5 and add.)
You will solve for quarters and then you can find nickels
Let's use algebra to solve this problem step-by-step.
Let's assume that the number of nickels is represented by 'N', and the number of quarters by 'Q'.
From the given information, we have two equations:
1) N + Q = 31 (Equation 1) - total number of coins
2) 0.05N + 0.25Q = 4.55 (Equation 2) - total value of coins
Now, let's solve this system of equations step-by-step using substitution or elimination method.
Using the substitution method:
From Equation 1, we can write N = 31 - Q.
Substituting N in Equation 2:
0.05(31 - Q) + 0.25Q = 4.55
Simplifying the equation:
1.55 - 0.05Q + 0.25Q = 4.55
Combining like terms:
0.20Q = 3.00
Dividing both sides by 0.20:
Q = 15
Now, substitute the value of Q back into Equation 1:
N + 15 = 31
Subtracting 15 from both sides:
N = 16
Therefore, there are 16 nickels in the desk.
To find the number of nickels, we need to set up a system of equations based on the information given.
Let's represent the number of quarters as 'q' and the number of nickels as 'n'.
From the problem, we have two equations:
1) The total number of coins is 31:
q + n = 31
2) The total value of the coins is $4.55:
0.25q + 0.05n = 4.55
Now we can solve this system of equations.
First, let's solve the first equation for q by subtracting n from both sides:
q = 31 - n
Now substitute this expression for q into the second equation:
0.25(31 - n) + 0.05n = 4.55
Distribute 0.25:
7.75 - 0.25n + 0.05n = 4.55
Combine like terms:
-0.20n + 7.75 = 4.55
Subtract 7.75 from both sides:
-0.20n = -3.20
Divide both sides by -0.20 to solve for n:
n = -3.20 / -0.20
n = 16
So, Mrs. Boyd has 16 nickels.