Two friends sold many pieces of furniture and made $860 during their garage sale. They had twelve more $10 bills than $50 bills. They had 1 more then 3 times as many $20 bills as $50 bills. How many of each denomination did they have?

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let the number of $50 be x; therefore, the two friends had 12+x numbers of $10, and 3x+1 number of $20.

However, they made $860 in total. Therefore, multiply the number of notes by the note's value to get $860.

$50x + $10(12+x) + $20(3x+1)= $860, opening the brackets we have;

$50x+$120+$10x+$60x+$20=$860

collecting like terms, then;

$50x+$60x+$10x=$860-$20-$120

$120x=720, divide both sides by $120;

x=6

the two friends had six $50 denomination,

12+6= 18, and eighteen $10 denominations,

3(6)+1=18+1=19, and nineteen $20 denominations.

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