Luis has$ 10.25 in change in his piggy bank.the number of nickles is three times the number of dimes the number of quaters is one how many coins does he have.
.05N+.1D=10.25
N=3D
solve for N, D, then the number of coins is N+D
So 10.25=0.05n+0.1d+0.25q
n=3d
q=4*d+1
Substitute d and q to the top equation
So 10.25=0.05(3d)+0.1d+0.25(4*d+1)
Distribute 10.25=0.15d+0.1d+1d+0.25
Simplify 10.25=1.25d+0.25
10.25-0.25=1.25d --> 10/1.25=d--> d=8
plug 8 back into the equations
3*8=n --> n=24
4*8+1=q --> q=33
If you replace all the variables with the numbers, you should get 10.25
To find the number of coins Luis has, we can set up a system of equations. Let's denote the number of nickels as "n," the number of dimes as "d," and the number of quarters as "q."
Given that the number of nickels is three times the number of dimes, we can express this relationship as:
n = 3d Equation 1
And we are also told that the number of quarters is one. We can write this as:
q = 1 Equation 2
Now, we need to consider the total value of the coins. Each nickel is worth $0.05, so the value of all the nickels can be expressed as 0.05n. Similarly, each dime is worth $0.10, so the value of all the dimes is 0.10d. Lastly, each quarter is worth $0.25, so the value of all the quarters is 0.25q.
Since Luis has a total of $10.25 in change, we can write the equation:
0.05n + 0.10d + 0.25q = 10.25 Equation 3
Now we have a system of three equations:
n = 3d
q = 1
0.05n + 0.10d + 0.25q = 10.25
We can now solve this system to find the values of n, d, and q.