I have19 coins that are worth a total of $1.10.If they consist only of dimes and nickels, then how many nickels do I have?
n + d = 19 so d = 19-n
5n + 10 d = 110 cents
5 n + 10(19-n) = 110
5 n + 190 -10 n = 110
-5 n = -80
n = 16
you are right but to explain a little more you would need to show your steps on how you got the dimes for it to make more sense like this.
d= number of dimes
10d= amount of dimes
n= number of nickels
5d= amount of nickels
d+n =19
10d+5n= 1.10
n=19-d = # of nickels so...
10d+5(19-d)=1.10 solving...
10d+95-5d=1.10
5d=15 and then divided each side by 5 and get 3 dimes. To get the number of nickels all you would have to do is subtract 19 from 3 and get 16 nicles and that would be it
To solve this problem, we can set up a system of equations.
Let's represent the number of dimes as 'd' and the number of nickels as 'n'.
The first equation represents the total number of coins:
d + n = 19
The second equation represents the total value of the coins in dollars:
0.10d + 0.05n = 1.10
To solve this system of equations, we can use substitution or elimination method. Let's use substitution method here.
From the first equation, we have d = 19 - n.
Substituting this value of d into the second equation:
0.10(19 - n) + 0.05n = 1.10
1.90 - 0.10n + 0.05n = 1.10
Combine like terms:
0.05n = 1.10 - 1.90
0.05n = -0.80
Divide both sides by 0.05:
n = -0.80 / 0.05
n = -16
However, since the number of coins (n) cannot be negative, this means that there is an error in the given information or the way the problem is formulated. Please double-check the question or provide additional details if available.