number of $ bills to equal 9550

Question

a stack of $20, $50, and $100 bills were confiscated. There were 46 more $50 bills than $100 bills. also, the number of $20 bills was 7 times the number of $100 bills. The total value was $9550. Find the number of each type of bill.

Answer 1

let x = the number of $100 bills

 

x + 46 = the number of $50 bills

 

7x = the number of $20 bills

 

100x + 50(x + 46) + 20(7x) = 9550

 

100x + 50x + 2300 + 140x = 9550

 

290x + 2300 = 9550

 

290x = 7250

 

x = 25

 

There are 25 one hundred dollar bills, x + 46 = 25 + 46 = 71 fifty dollar bills, and 7x = 7 * 25 = 175 twenty dollar bills

 

 

Answer 2

t= $20

f = $50

h = $100

 

f = h + 46

t = 7h

20t + 50f + 100h =9550

 

Plus the first 2 into the last and solve.

 

20(7h) + 50(h+46) + 100h = 9550

140h + 50h + 2300 + 100h = 9550

290h = 7250

h = 25

 

f = 25 + 46 = 71

t = 7*25 = 175

 

Let's check those answers.

 

20(175) + 50(71) + 100(25) =9550

3500 + 3550 + 2500 = 9550

9550 = 9550