Urgent Algebra 1 money problem

Question

The boys have a small game going in the backroom. Mr. X decides to pull out and finds he has $194. If he has four times as many $1 bills as $5 bills, one-fifth as many $2 as $5 bills, and the same number of $50 bills as $2 bills, how many bills of each kind does he have?

Answer 1

It is a system of 4 variables with 4 equations:

Let number of bills

$1 - a

$2 - b

$3 - c

$50 - d

The system of 4 equation with 4 variables:

⌈ a = 4c => a = 4c

| b = c/5 => b = c/5

| d = b => d = c/5

⌊ a + 2b + 5c + 50d =194 => 4c + 2c/5 + 5c + 50c/5 = 194

Solve by substitution ( I picked c)

c * (4+2/5 + 5 + 10) = 194

c = 10

So, the answer is :

$1 : 40

$2 : 2

$5 : 10

$50 : 2