Question

a bill folder holds one dollar , five dollar, ten dollar and has a value of $210 . there are 50 bills total were the number of one dollar bills is one less than twice the number of five dollar bills . apply lu decomposition method to determine how many of each bill are there

Answer 1

Answer:

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Answer 2

Answer:

25 of one dollar bills, 13 of five dollar bills, 12 of ten dollar bills.

Step-by-step explanation:

You can write the following equations:

x+y+z=50 (1)

x+5y+10z= 210 (2)

x= 2y-1 (3)

x= number of one dollar bills

y= number of five dollar bills

z= number of ten dollar bills

Then, you can replace (3) in (1) and (2):

2y-1+y+z= 50

3y+z=51

2y-1+5y+10z= 210

7y+10z=211

From that, you will get the following equations:

3y+z=51 (4)

7y+10z=211 (5)

Now, you have to isolate z in (4) and replace it in (5):

z= 51-3y

7y+10(51-3y)=211

7y+510-30y=211

-23y=-299

y= 13

Then, replace the value of y in z= 51-3y:

z=51-3(13)= 51-39= 12

After this, you can replace the value of y in (3):

x=2(13)-1= 26-1= 25

According to this, the answer is that there are 25 of one dollar bills, 13 of five dollar bills, 12 of ten dollar bills.