What is the combined monetary value…….?
Canadian 10¢ and 25¢ coins are made of pure nickel which has a density of 8.902 g/cm3. Suppose each dime weighs 2.08 g and each quarter weighs 5.20 g. A small collection of dimes and quarters are submerged in 10.00 mL of water in a graduated cylinder causing the water level to rise to the 17.13 mL mark. What is the combined monetary value (in Can$) of those coins?
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1 dime occupies 2.08 g / (8.902 g/cm3) = 0.234 cm3
1 quarter occupies 5.20 g / (8.902 g/cm3) = 0.584 cm3
The coins have displaced 17.13 - 10.00 mL = 7.13 mL of water
The maximum possible number of dimes = 7.13 / 0.234 = 30
The maximum possible number of quarters = 7.13 / 0.584 = 12
For which positive integers D and Q is this equation balanced?:
0.234 D + 0.584 Q = 7.13
There are several near solutions, but all have a combined monetary value of Can$ 3.05.
The solutions are:
D Q
3 11
8 9
13 7
18 5
23 3
28 1