Question

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?

Answer 1

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.

Answer 2

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