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olga2289
8 days ago
10

A billfold holds one-dollar, five-dollar, and ten-dollar bills and has a value of $210. There are 50 bills total where the numbe

r of one-dollar bills is one less than twice the number of five-dollar bills. How many of each bill are there? Write your answer as an ordered triple in the form (# of one dollar bills, # of five dollar bills, # of ten dollar bills).
Mathematics
1 answer:
AnnZ [9K]8 days ago
3 0

Answer:

25 one-dollar bills, 13 five-dollar bills, and 12 ten-dollar bills.

Step-by-step explanation:

The equations that can be formed are:

x+y+z=50 (1)

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

x= 2y-1 (3)

where x = number of one-dollar bills,[tag_20] y = number of five-dollar bills,

z = number of ten-dollar bills

Substituting (3) into (1) and (2) gives:[

2y-1+y+z= 50

3y+z=51

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

7y+10z=211

You will then derive the following equations:

3y+z=51 (4)

7y+10z=211 (5)

Next, isolate z using (4) and substitute it into (5):

z= 51-3y

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

7y+510-30y=211

-23y=-299

y= 13

After substituting the value of y into z= 51-3y, we find:

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

Now, replace y's value in (3):

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

Thus, the final result indicates there are 25 one-dollar bills, 13 five-dollar bills, and 12 ten-dollar bills.

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