June has $1.95 in dimes and nickels. She has a total of 28 coins. How many dimes and how many nickels does she have?
D+N=28
10D+ 5N=195
Does that help?
d + n = 28
10d + 5n = 195
solve the system
... substitution or elimination
To solve this problem, let's set up a system of equations. Let's represent the number of dimes as 'd' and the number of nickels as 'n'.
We know that the total value of the coins is $1.95, which can be expressed as:
0.10d + 0.05n = 1.95 (equation 1)
We also know that the total number of coins is 28, so we can write:
d + n = 28 (equation 2)
To solve this system of equations, we can use either the substitution or elimination method. Let's use the substitution method.
We can solve equation 2 for d:
d = 28 - n
Now substitute this value of d into equation 1:
0.10(28 - n) + 0.05n = 1.95
Distribute:
2.80 - 0.10n + 0.05n = 1.95
Combine like terms:
-0.05n = -0.85
Divide both sides by -0.05:
n = 17
Now substitute the value of n back into equation 2 to find d:
d + 17 = 28
d = 28 - 17
d = 11
So June has 11 dimes and 17 nickels.