SOLUTION: There are 35 coins in a jar. There are a combination of loonies and quarters. The Value of the coins is 17.75. How many loonies are there? This is how I attempted this.. however it

Question 858207: There are 35 coins in a jar. There are a combination of loonies and quarters. The Value of the coins is 17.75. How many loonies are there? This is how I attempted this.. however it does not make sense... as I know there has to be 12 loonies.... How would I do this using an equation??
100L + 25(35-L) = 1775
100L + 875 - 25l = 1775
75l+875=1175
75L + 300
75L/75 + 300/75
L=4

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
This is not a linear system, at least not how I analyze it.

Let Q = how many quarts
let L = how many loonies
let r = rate of dollars per coin for the loonies; we already know that for the quarters, that rate is 0.25. We do not yet know this rate for loonies.

Coin Count:
Dollars Count:
No other equation was found possible. We only know that Q, and L, must be Natural Numbers, and less clear about r, except it is greater than zero, and rational.

Solving the system symbolically for r will give:
...

So, this comes from a nonlinear system in three unknowns for two equations. The only way I see to find any possible reasonably answer is the crudely test values of Q from 34 to 1; compute r for each value of Q. We must have values of r such that r is rational, and r greater than 0. A simple computer program might be the way to go, or maybe use the formula in a graphing calculator.

NOTE: You may find several possible answers for this. I just checked a couple different values for r from the equation above just found. If Q is 33, then you find r = 9 dollars per loony. Other values for Q may also be useful. The question as given seems to be open-ended.
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