A pencil, an eraser, and a notebok together cost one dollar.
A notebook costs more than two pencils.
Three pencils cost more than four erasers.
Three erasers cost more than a notebook.
How much does each cost ?
Given:
P + E + N = 100 cents
N > 2 P
3 P > 4 E
3 E > N
3 P > 4 E → 2 P > 8/3 E
N > 2 P → N > 8/3 E
N < 3 E (given)
Therefore:
8/3 E < N < 3 E
3P > 4 E → P > 4/3 E
2P < N → P < N/2
N < 3 E → N/2 < 3/2 E
Therefore:
4/3 E < P < 3/2 E
Converting those to sixths, we have
16/6 E < N < 18/6 E or N = roughly 17 / 6 E
8/6 E < P < 9/6 E or P = roughly 8.5 / 6 E
Now try some values for E:
E
P
N
Total
6
8.5
17
31.5
12
17
34
63
18
25.5
51
94.5
That's close to 100, so with a bit of fiddling, we can make it:
E = 19
P = 26
N = 55
Total = 100
Checking the conditions: N > 2 P ? ... 55 > 2 * 26 ? ... .. 55 > 52 ... yes 3 P > 4 E ? . 3 * 26 > 4 * 19 ? . 78 > 76 .. yes 3 E > N ? ... 3 * 19 > 55 ? ... .. 57 > 55 ... yes
