|
Question 881753: 1. State the variables
2. Write a system of equations
3. Write a matrix equation
4. Solve the equation using inverse matrices with a calculator
5. Answer the question
3. You have $3.80 in change in your pocket. You have a total of 25 coins in your pocket which consist of nickels, dimes, and quarters. If you have one more dime than quarters, how many of each coin do you have?
______________Nickels ___________Dimes Quarters_________
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! No similar problems.
One problem at a time.
n+d+q=25
.05n+.10d+.25q=3.80
0n+1d-1q=1
1,1,1,25
5,10,25,380
0,1,-1,1
Your matrix
№ n d q b
1 1 1 1 25
2 5 10 25 380
3 0 1 -1 1
Write the main matrix
№ n d q
1 1 1 1
2 5 10 25
3 0 1 -1
Determinant is not zero, therefore inverse matrix exists
Calculate the inverse matrix
n d q
1.4 -0.08 -0.6
-0.2 0.04 0.8
-0.2 0.04 -0.2
Multiply the inverse matrix by the solution vector
№ X
n 4
d 11
q 10
n = 4
d = 11
q= 10
|
|
|
| |
