15 postcards, 10 envelopes, and a notepad cost 1 dollar and 68 cents. The envelope is 8 times cheaper than the notepad and 2 cents more expensive than the postcard. What is the price of the postcard, the envelope and the notepad?

First, we have a cost expression for all of the items.

168 = 15p + 10e + n, where p = postcard price, e = envelope price, and n = notepad price in cents.

We can create expressions for the three objects in terms of the cost of the envelope, from the information given in the prompt:

n = 8e

p = e-2

Substituting into the original equation:

168 = 15 (e-2) + 10e + 8e = 15e - 30 + 10e + 8e = 33e - 30

Thus 198 = 33e and e = 6 cents.

Going back to the original expressions:

e = 6 cents

n = 8e = 48 cents

p = e-2 = 4 cents

Thus the prices of the postcard, envelope, and notepad are 4, 6, and 48 cents, respectively.

This is the concept of algebra. Let the price of envelope be $x;

the price of notepad is $ 8x

the price of postcard is $ (x-0.02)

the total amount is $1.68

thus:

x+8x + (x-0.2) = 1.68

10x-0.02=1.68

10x=1.68+0.02

10x=1.7

thus

x=0.17

hence the price of an envelope is x=$0.17 = 17 cents

the price of notepad is 8x=0.17*8=$1.36

the price of a postcard is x-0.02=0.17-0.02=$0.15 = 15 cents