Applications of Linear Systems

Question

Kerry asked a bank teller to cash a $390 check using $20 bills and $50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive?

Answer 1

Hi Sean, Let x represent the $20 bills and y represent the $50 bills. Create two equations representing the information given.

 

Equation 1, number of bills:

 

x + y = 15

 

Equation 2, value of bills:

 

20x + 50y = 390

 

To solve by substitution:

 

x + y = 15

 

x = 15 - y

 

Substitute for x in equation 2:

 

20 * (15 - y) + 50y = 390

 

300 - 20y + 50y = 390

 

Combine terms:

 

30y = 90

 

y = 3

 

The teller gave Kerry 3 $50 bills.

 

x + y = 15

 

x + 3 = 15

 

x = 12

 

The teller gave Kerry 12 $20 bills.

 

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