I need help with math

Question

Neil has a total of twelve $5 and $10 bills in his wallet. He has

5 times as many $10 bills as $5 dollar bills. How many of each does he have?

Answer 1

There is a ratio given. " He has 5 times as many $10 bills as $5 dollar bills."

That means he has one of the following:

$1-d $10-d total

------ -------- -------

1 5 6

2 10 12

Neil has 12 bills -- 2 1-dollar bills and 10 $10-dollar bills.

Now, to solve this using algebra:

Let T = number of $10-dollar bills

D = number of $1-dollar bills

T = 5D [eq1]

T + D = 12 [eq2]

Substitute eq1 into eq2:

5D + D = 12

6D = 12 [combine like terms]

D = 2 [divide both sides by 2]

Neil has 2 $1-bills. Neil has 10 $10-bills. That's 12 bills in all.