i have 50 coins in quarters and nickels. if the total value is $5.90, how many of each coin do i have ?
start out with what you know
-so you have a total of 50 coins
-a quarter is equal to 25c
-a nickel is eqal to 5c
0.25*4=$1.00
0.25*12=$3.00
0.25*16=$4.00
0.25*20=$5.00
0.05*20=$1.00
20+16=36 50-36=14
This might help
You know you have at least 3 nickels, because only $5.75 can be made with just quarters. So, you have at most 47 quarters.
47 quarters = $11.75
plus 3 nickels = $11.90
That is $6.00 too much.
Each quarter replaced by a nickel reduces the value by 20 cents.
Since you have $6.00 too much, replace 30 quarters with nickels. That leaves
17 quarters + 33 nickels.
$4.25 + $1.65 = $5.90
To solve this problem, we can set up a system of linear equations. Let's denote the number of quarters as 'q' and the number of nickels as 'n'.
We have two equations based on the given information:
1) q + n = 50 (equation 1) - as there are a total of 50 coins.
2) 0.25q + 0.05n = 5.90 (equation 2) - as the total value of the coins is $5.90.
Now, we can use a method called substitution to solve the system of equations.
First, let's rearrange equation 1 to solve for 'q':
q = 50 - n
Now, substitute this value for 'q' in equation 2:
0.25(50 - n) + 0.05n = 5.90
Distribute the 0.25:
12.50 - 0.25n + 0.05n = 5.90
Combine the 'n' terms:
12.50 - 0.20n = 5.90
Next, isolate the 'n' term on one side by subtracting 12.50 from both sides:
-0.20n = 5.90 - 12.50
Simplify:
-0.20n = -6.60
Now, divide both sides by -0.20 to solve for 'n':
n = (-6.60) / (-0.20)
Calculate:
n = 33
Now that we have the value of 'n', we can substitute it back into equation 1 to find 'q':
q = 50 - n = 50 - 33 = 17
Therefore, you have 17 quarters and 33 nickels.