Question

Part of the proceeds from a garage sale was ​$275 worth of ​$5 and ​$20 bills. If there were 5 more ​$5 bills than ​$20 ​bills, find the number of each denomination. There were nothing ​$5 bills and nothing ​$20 bills.

Answer 1

Let x be the number of $20 bills.

$20x will then be the amount of money that the $20 bills make up.
$5(x + 5) will then be the amount of money that the $5 bills make up, since there are 5 more $5 bills than $20 bills.

$275 = $20x + $5(x + 5)
{Expand the equation}
$275 = $20x + $5x + $25
{Subtract both sides of equation by $25}
$275 - $25 = $20x + $5x
$250 = $25x
$25x = $250
{Make x the subject of equation}
x = $250 ÷ $25
{Dollar symbols cancel out}
x = 10
Thus, there are 10 $20 bills.

Then, number of $5 bills is:
x + 5
= 10 + 5
= 15
There are 15 $5 bills.

Hope this helps! :)