# 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