a stack of $20, 50$, and$100 bills were retrieved as a part of a police investigation. there were 43 more 50

Question

A STACK OF 20, 50 AND 100$ BILLS WERE RETRIEVED AS PART OF A POLICE INVESTIGATION. THERE WERE $43 MORE 50$ BILLS THEN 100$ BILLS. ALSO THE NUMBER OF 20$ BILLS WAS 3 TIMES THE NUMBER OF $100 BILLS. OF THE TOTAL OF THE VALUE OF THE MONEY WAS 7610. FIND THE NUMBER OF EACH TYPE OF BILL

Answer 1

Let x = the # of $20 bills

Let y = the # of $50 bills

Let z = the # of $100 bills

 

"There were 43 more $50 bills than $100 bills" translates into y = z + 43

 

"The number of $20 bills was 3 times the number of $100 bills" translates into x = 3z

 

"The total of the value of the money was $7610" translates into 20x + 50y + 100z = 7610

 

We now have a system of 3 equations with 3 unknowns:

y = z + 43

x = 3z

20x + 50y + 100z = 7610

 

Substituting the first two equations into the 3rd equations gives us:

20(3z) + 50(z+43) + 100z = 7610

60z + 50z + 2150 + 100z = 7610

210z = 5460

z = 26

y = 26 + 43 = 69

x = 3(26) = 78

 

Check:

20x + 50y + 100z = 7610

20(78) + 50(69) + 100(26) = 1560 + 3450 + 2600 = 7610