Two friends sold many pieces of furniture and made $1610 during their garage sale. They had fifteen more $10 bills than $50 bills. They had 1 more than three times as many $20 bills as $50 bills. How many of each denomination did they have?
Let
w = # fifties
x = # twenties
y = # tens
Then we know that
50w+20x+10y = 1610
y = w+15
x = 3w+1
Now just solve for w,x,y
Let's start by assigning variables to the unknown quantities:
Let's represent the number of $50 bills as "x."
Then the number of $10 bills would be "x + 15" (since they have fifteen more $10 bills than $50 bills).
And the number of $20 bills would be "3x + 1" (since they have one more than three times as many $20 bills as $50 bills).
Now let's set up equations based on the given information:
50x + 10(x + 15) + 20(3x + 1) = 1610
Now we can solve for x by simplifying and solving the equation:
50x + 10x + 150 + 60x + 20 = 1610
120x + 170 = 1610
120x = 1610 - 170
120x = 1440
x = 1440 / 120
x = 12
Therefore, there are 12 $50 bills. Hence,
Number of $10 bills = x + 15 = 12 + 15 = 27
Number of $20 bills = 3x + 1 = 3(12) + 1 = 37
So, they had 12 $50 bills, 27 $10 bills, and 37 $20 bills.
To solve this problem, let's break it down and set up equations based on the given information:
Let's assume the number of $50 bills = x
Then the number of $10 bills = x + 15 (since they had fifteen more $10 bills than $50 bills)
And the number of $20 bills = 1 + 3x (since they had 1 more than three times as many $20 bills as $50 bills)
Now, let's calculate the total amount of money from each bill denomination:
$50 bills: x * $50 = 50x
$10 bills: (x + 15) * $10 = 10(x + 15)
$20 bills: (1 + 3x) * $20 = 20(1 + 3x)
The total amount of money from all the bills is $1610, so we can set up the equation:
50x + 10(x + 15) + 20(1 + 3x) = 1610
Now, let's solve the equation:
50x + 10x + 150 + 20 + 60x = 1610
80x + 170 = 1610
80x = 1610 - 170
80x = 1440
x = 1440 / 80
x = 18
So, they had 18 $50 bills. Using that information, we can calculate the number of $10 bills and $20 bills:
Number of $10 bills = x + 15 = 18 + 15 = 33
Number of $20 bills = 1 + 3x = 1 + 3*18 = 1 + 54 = 55
Therefore, they had 18 $50 bills, 33 $10 bills, and 55 $20 bills.