John has $2.50 in nickels and dimes in his wallet. He has twice as many dimes as nickels. How many of each coin does he have? Let dimes = _____. Let nickels = _______. Equation:________________
If dimes = D and nickels equals N, and we let D = 2N,
Then 5 N + 10 D = 25 N = 250
Dimes=d Nickels=n
.05n + 0.1d = 2.50
d = 2n
0.05n + 0.1(2n) = 2.50
0.05n + 0.2n = 2.50
0.25n = 2.50
n = 2.50/0.25
n=10
d=20
There are 10 nickels and 20 dimes.
To find the number of dimes and nickels John has, we can set up a system of equations based on the given information.
Let's start by assigning variables to the unknowns:
Let dimes = D
Let nickels = N
We are given two pieces of information to form equations:
1. "John has $2.50 in nickels and dimes in his wallet":
The value of the dimes (D) in cents is equal to 10 times the number of dimes.
So the value of dimes in cents is 10D.
The value of the nickels (N) in cents is equal to 5 times the number of nickels.
So the value of nickels in cents is 5N.
The total value of the coins in cents is $2.50, which is equal to 250 cents.
So the equation for the total value of the coins is: 10D + 5N = 250.
2. "He has twice as many dimes as nickels":
This statement tells us that the number of dimes (D) is twice the number of nickels (N).
So the equation representing this information is: D = 2N.
Now we have a system of two equations:
Equation 1: 10D + 5N = 250
Equation 2: D = 2N
We can substitute Equation 2 into Equation 1 to solve for the variables.
Substituting D = 2N into Equation 1, we get:
10(2N) + 5N = 250
20N + 5N = 250
25N = 250
N = 10
Now, substituting N = 10 into Equation 2, we get:
D = 2(10)
D = 20
Therefore, John has 20 dimes (D) and 10 nickels (N).
Answer:
Let dimes = 20.
Let nickels = 10.
Equation: 10(20) + 5(10) = 250.