Solve the following problem using a matrix equation and inve

Solve the following problem using a matrix equation, and inverse matrix.

If there are 60 dimes and nickels worth $4.30 altogether, how many of each are there? What about 50 coins worth $4.00? 63 coins worth $5.25?

let number of dimes be x and number of nickels be y

then, x+y=60

one dime=10 cents and one nickel=5 cents

10x+5y=480

putting above two equations in matrices, [1 1] [x] =[60]

[10 5] [y] [480]

this becomes AX=B

X=A^-1B

Taking inverse matrix, X=1/-5 [5 -1] [60]

[-10 1] [480]

X=1/-5[300-480]

[-600+480]

X=[36]

[24]

x= 36 y =24

number of dimes=36

number of nickels=24