Question

A cash register contains only five dollar and fifty dollar bills. It contains four times as many five dollar bills as fifty dollar bills, and the total amount of money in the cash register is $3,430. How many five dollar bills are in the cash register?

Answer 1

The cash register contains 196 five dollar bills. We determined this by setting up a system of linear equations using the given total amount and the relationship between the numbers of five and fifty dollar bills.

Step-by-step explanation:

The question involves solving a system of linear equations to determine the number of five dollar bills and fifty dollar bills in a cash register. The total amount of money is given as $3,430, with the number of five-dollar bills being four times the number of fifty-dollar bills.

Let's denote the number of fifty-dollar bills as x and the number of five-dollar bills as 4x. Since each fifty-dollar bill is worth $50, for the x fifty-dollar bills in the register, the total value is $50x. Similarly, for the 4x five-dollar bills, the total value is $5(4x) or $20x. Combined, the total value is $50x + $20x, which equals the total amount in the cash register, $3,430.

Adding the values of $50x and $20x together, we get:

$50x + $20x = $3,430

Simplify the equation by combining like terms:

$70x = $3,430

Divide both sides of the equation by $70 to find the value of x:

x = $3,430 / $70

x = 49

Now that we have the value of x, the number of fifty-dollar bills, we can find the number of five-dollar bills:

4x = 4 × 49

4x = 196

So, there are 196 five-dollar bills in the cash register.