Question

a change machine at an arcade gives change for $1 bills and $5 bills. if during a particular day, 200 bills were inserted into the machine, and the total value of the bills was $300, how many $1 bills were inserted into the machine?
a. 25
b. 75
c. 125
d. 175

Explanation:

Step1: Define variables

Let $x$ = number of $1 bills, $y$ = number of $5 bills.

Step2: Set up total bills equation

$x + y = 200$

Step3: Set up total value equation

$1x + 5y = 300$

Step4: Solve the system of equations

Rearrange Step2: $x = 200 - y$. Substitute into Step3:
$200 - y + 5y = 300$
$200 + 4y = 300$
$4y = 100$
$y = 25$
Substitute $y=25$ back into $x = 200 - y$:
$x = 200 - 25 = 175$

Answer:

D. 175