A nation has five types of coins: sinds, dalts, lorgs, harps, and plunks. 1 sind = 4 lorgs
2 plunks = 5 dalts
5 sinds = 2 harps
1 plunk = 3 harps

Which coin is the most valuable?

a) sind
b) dalt
c) harp
d) plunk

Work Shown:

When comparing units like inches, feet and yards, we need to get everything in the same unit to make a valid comparison. So we'd need to convert everything to inches for instance. The same idea applies to these five coins. We need to get everything in either lorgs, sinds, plunks, harps or dalts (pick one of those five).

It's effectively the same as trying to convert dollars into cents (eg: $1.37 converts to 137 cents). Or you can think of it as 1 dollar = 100 cents, 1 quarter = 25 cents, 1 dime = 10 cents, and so on.

The steps in the various sections below will aim to get all the coins converted to lorgs as our base unit. I found the lorg coin to be the smallest of value through trial and error, which is why I'm aiming to get everything in terms of lorgs.

The four given equations are

I'll refer to them as equation (1) through equation (4) in that order above.

1 sind = 4 logs equation (1)

5 sinds = 20 lorgs multiply both sides by 5

2 harps = 20 lorgs replace "5 sinds" with "2 harps" from equation (3)

1 harp = 10 lorgs divide both sides by 2; call this equation (5)

1 plunk = 3 harps equation (4)

1 plunk = 3*(1 harp)

1 plunk = 3*(10 lorgs) plug in equation (5)

1 plunk = 30 lorgs call this equation (6)

2 plunks = 5 dalts equation (2)

5 dalts = 2 plunks

5 dalts = 2*(1 plunk)

5 dalts = 2*(30 lorgs) replace 1 plunk with 30 lorgs; see equation (6)

5 dalts = 60 lorgs

1 dalt = 12 lorgs divide both sides by 5; call this equation (7)

We found the following conversions:

Each of those equations helps us see how much the value of the coins sind, dalt, harp, plunk are in terms of lorgs.

We can see that 1 plunk yields the most lorgs at 30. So the plunk coin is the most valuable. The lorg coin is least value since you need 4 of those coins to make the second lowest coin of 1 sind.

The order of the coins value from least to greatest is: lorg, sind, harp, dalt, plunk.

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.