A bank teller has 35 bills in $5, $10, and $20 denominations. The total value from these bills is $370.The total number of $10 bills and $20 bills is 7more than the number of $5. How many bills of each denomination?

No. of $5=bills a, $10 bill=b and $20 bill=c

Then a+b+c=35
5a+10b+20c=370, and
b+c=a+7.

Substituting value of b+c in first eq.,
a+(a+7)=35 or 2a=28 or a=14 and
b+c=35-14=21.
Substituting value of a in second eq., 14x5+10b+20c=370 or 10b+20c=370-70
Or 10b+20c=300 or b+2c=30
Subtract from this the eq. b+c=21 and we get c=30-21=9. thus b=35-14-9=12.
Check:14x5+12x10+9x20=370
70+120+180=370 OK.

To find out how many bills of each denomination the bank teller has, we can set up a system of equations based on the given information.

Let's assign variables to represent the number of each type of bill:
- Let x represent the number of $5 bills.
- Let y represent the number of $10 bills.
- Let z represent the number of $20 bills.

We know that there is a total of 35 bills, so the first equation is:
x + y + z = 35 (equation 1)

We also know that the total value of the bills is $370. We can express this as a second equation:
5x + 10y + 20z = 370 (equation 2)

Lastly, we're given the information that the total number of $10 bills and $20 bills is 7 more than the number of $5 bills:
y + z = x + 7 (equation 3)

Now we have a system of three equations with three variables. We can solve this system to find the values of x, y, and z.

One way to solve the system is through substitution. Let's solve equation 3 for x:
x = y + z - 7

We can substitute this expression for x in equations 1 and 2:
(y + z - 7) + y + z = 35 (equation 1)
5(y + z - 7) + 10y + 20z = 370 (equation 2)

Simplifying equation 1:
2y + 2z = 42
y + z = 21 (equation 4)

Simplifying equation 2:
5y + 5z - 35 + 10y + 20z = 370
15y + 25z = 405
3y + 5z = 81 (equation 5)

We now have a simpler system with equation 4 and equation 5.

To solve this system, we can multiply equation 4 by 3 to eliminate the y term:
3(y + z) = 3(21)
3y + 3z = 63 (equation 6)

Subtracting equation 6 from equation 5:
(3y + 5z) - (3y + 3z) = 81 - 63
2z = 18
z = 9

Substituting z = 9 into equation 4:
y + 9 = 21
y = 12

Substituting y = 12 and z = 9 into equation 1:
x + 12 + 9 = 35
x + 21 = 35
x = 14

Therefore, the bank teller has 14 $5 bills, 12 $10 bills, and 9 $20 bills.