I have 37 coins, nickels dimes, quarters that equal 5.50 . I have 4 more quarters than dimes . How many nickels do I have?
n+d+q = 37
5n+10d+25q = 550
q = d+4
n + d + d+4 = 37
5n + 10d + 25(d+4) = 550
n + 2d = 33
5n + 35d = 450
5n + 10d = 165
5n + 35d = 450
25d = 285
Is there a typo somewhere?
To solve this problem, we'll need to set up equations based on the given information, and then find the values that satisfy those equations.
Let's denote the number of nickels as N, the number of dimes as D, and the number of quarters as Q.
We know that the total number of coins is 37: N + D + Q = 37.
We also know that the value of all the coins together is $5.50: 0.05N + 0.1D + 0.25Q = 5.50.
Additionally, we're told that there are 4 more quarters than dimes: Q = D + 4.
Now we have a system of equations that we can solve simultaneously to find the values of N, D, and Q.
Let's substitute Q in the first equation with D + 4:
N + D + (D + 4) = 37.
Combining like terms:
N + 2D + 4 = 37.
Next, let's rearrange the equation and write it in terms of N:
N = 37 - 2D - 4.
Simplifying further:
N = 33 - 2D.
Now, substitute the value of N in the second equation:
0.05(33 - 2D) + 0.1D + 0.25(D + 4) = 5.50.
Distribute and combine like terms:
1.65 - 0.1D + 0.1D + 0.25D + 1 = 5.50.
Combine like terms again:
0.35D + 2.65 = 5.50.
Subtract 2.65 from both sides:
0.35D = 2.85.
Now, divide both sides by 0.35:
D = 2.85 / 0.35 ≈ 8.14.
Since D represents the number of dimes, we can round it to the nearest whole number, which is 8.
Now, substitute D = 8 into the equation N = 33 - 2D:
N = 33 - 2(8) = 33 - 16 = 17.
Finally, to find the number of nickels, substitute N = 17 into the first equation:
17 + 8 + Q = 37.
Simplify and solve for Q:
Q = 12.
Therefore, you have 17 nickels.