there are 20 coins made up of nickles and dimes the total value is 1.75
number of nickels ---- x
number of dimes = 20-x
Value of money equation:
5x + 10(20-x) = 175
solve for x
10
To find the number of nickels and dimes in a collection of coins, and their respective values, we can use a system of equations.
Let's say the number of nickels is represented by "n" and the number of dimes is represented by "d".
From the problem statement, we know that there are a total of 20 coins, so we can write our first equation as:
n + d = 20
We also know that the total value of the coins is $1.75. Since one nickel is worth $0.05 and one dime is worth $0.10, we can write a second equation for the total value:
0.05n + 0.10d = 1.75
Now we have a system of two equations:
n + d = 20
0.05n + 0.10d = 1.75
We can use various methods to solve this system of equations, such as substitution, elimination, or matrices. Let's solve it using the substitution method:
From the first equation, we can express n in terms of d:
n = 20 - d
Substituting this expression for n into the second equation:
0.05(20 - d) + 0.10d = 1.75
Now, we can solve for d:
1 - 0.05d + 0.10d = 1.75
0.05d = 0.75
d = 0.75 / 0.05
d = 15
Now that we have the value for d (the number of dimes), we can substitute it back into the first equation to find the value of n:
n + 15 = 20
n = 20 - 15
n = 5
So, there are 5 nickels and 15 dimes in the collection of 20 coins.