two friends sold many pieces of furniture and made $1720 during the garage sale. They had fourteen more $10 bills than $50 bills. They had 4 more than two times as many $20 bills as $50 bills. How many of each denomination did they have?
number of fifties --- x
number of tens ---- x+14
number of twenties -- 2x+4
50x + 10(x+14) + 20(2x+4) = 1720
Solve for x, and all shall be revealed.
50x+10(x)+140+20(2x+4)=1720
50x+10x+140+40x+80=1720
100x+220=1720
100x=1720-220
x=1500/100
x=15
15 fifties
29 tens
34 twenties
Let's solve the problem step by step:
Step 1: Let's assume the number of $50 bills as 'x'.
Step 2: According to the given information, the number of $10 bills is 14 more than the number of $50 bills. So, the number of $10 bills would be 'x + 14'.
Step 3: The number of $20 bills is 4 more than twice the number of $50 bills. So, the number of $20 bills would be '2x + 4'.
Step 4: Now, let's calculate the total amount made from the garage sale. We can use the equation: Total amount = ($50 bills) + ($10 bills) + ($20 bills).
Total amount = 50x + 10(x + 14) + 20(2x + 4)
Step 5: Simplify the equation:
Total amount = 50x + 10x + 140 + 40x + 80
Step 6: Combine like terms:
Total amount = 100x + 140 + 80
Total amount = 100x + 220
Step 7: According to the problem, the total amount made from the garage sale is $1720. We can set up the equation:
100x + 220 = 1720
Step 8: Solve for 'x':
100x = 1720 - 220
100x = 1500
x = 15
Step 9: Now, substitute the value of 'x' back into the equations to find the number of each denomination:
Number of $50 bills = x = 15
Number of $10 bills = x + 14 = 15 + 14 = 29
Number of $20 bills = 2x + 4 = 2(15) + 4 = 34
Therefore, they had 15 $50 bills, 29 $10 bills, and 34 $20 bills.
To solve this problem, we can use algebraic equations. Let's represent the number of $50 bills as 'x'.
According to the problem, we know that there were fourteen more $10 bills than $50 bills. So, the number of $10 bills can be represented as '(x + 14)'.
We are also given that there were 4 more than two times as many $20 bills as $50 bills. Thus, the number of $20 bills can be represented as '2x + 4'.
Now, let's express the problem mathematically:
50x + 10(x + 14) + 20(2x + 4) = 1720
By simplifying the equation, we have:
50x + 10x + 140 + 40x + 80 = 1720
100x + 220 = 1720
Next, we subtract 220 from both sides of the equation:
100x = 1500
Dividing by 100 on both sides, we get:
x = 15
Therefore, there were 15 $50 bills. To find the number of $10 bills, we substitute the value of 'x' into '(x + 14)'.
Number of $10 bills = 15 + 14 = 29
To find the number of $20 bills, we substitute the value of 'x' into '2x + 4'.
Number of $20 bills = (2 * 15) + 4 = 30 + 4 = 34
So, they had 15 $50 bills, 29 $10 bills, and 34 $20 bills.