Question

Set up a linear system and solve. A cash register contains $5 bills and $50 bills with a total value of $345. If there are 15 bills total, then how many of each does the register contain?

Answer 1

6 $50 bills and 9 $5 bills

Explanation:

Let's let x = the number of $5 bills, and y = the number of $50 bills. With this, we can set up two equations:

5x + 50y = 345

x + y = 15

Because there is $345 total in the register, that means that 5 times the number of $5 bills plus 50 times the number of $50 bills would equal 345. And there are 15 bills total, so the numbers added is 15. Now, we can solve these equations through substitution:

x + y = 15

x = 15 - y

Now, plug in (15 - y) for x into the other equation, and solve for y:

5(15 - y) + 50y = 345

75 - 5 y + 50y = 345

75 + 45y = 345

45y = 270

y = 6

Since y is 6, that means we have 6 $50 bills. And there are 15 bills total, so there are 9 $5 bills. (15 - 6 = 9)