SOLUTION: How many quarters, dimes and pennies I need to total an amount of $3.27. Thank you. (needs a total of 20 coins)

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Question 957694: How many quarters, dimes and pennies I need to total an amount of $3.27. Thank you. (needs a total of 20 coins)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
q, d, p counts of the coins.
system%28q%2Bd%2Bp=20%2C0.25q%2B0.10d%2B0.01p=3.27%29

system%28q%2Bd%2Bp=20%2C25q%2B10d%2Bp=327%29

Expect more than one solution for how many of each coin. Two equations, THREE unknown variables. Use elementary row operations, but pick a variable to treat as a constant; best choice seems to be p.

Assuming p is a constant although not yet known value,
system%28q%2Bd=20-p%2C25q%2B10d=327-p%29-----simpler system
-
system%2825q%2B25d=25%2A20-25%2Ap%2C25q%2B10d=327-p%29
-
E1-E2,
15d=25%2A20-327-25p%2Bp
15d=173-24p
d=%28173-24p%29%2F15

Return again to simple system,
system%2810q%2B10d=10%2820-p%29%2C25q%2B10d=327-p%29
-
system%2810q%2B10d=200-10p%2C25q%2B10d=327-p%29

E2-E1,
15q=%28327-p%29-%28200-10p%29
15q=127%2B9p
q=%28127%2B9p%29%2F15


You want to find what whole number p will make q and d to be whole numbers, and also be sure that q+d+p=20 :
system%28d=%28173-24p%29%2F15%2Cq=%28127%2B9p%29%2F15%29