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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?

1 Answer

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Let's start by setting up some equations to represent the given information.

Let's say the price of a postcard is "x" cents.

Then, according to the problem statement, the price of an envelope is 8 times cheaper than the notepad, which means the price of an envelope is (1/8)th of the price of the notepad. So the price of an envelope is (1/8)*y cents, where "y" is the price of the notepad in cents.

Also, we know that the price of an envelope is 2 cents more expensive than the price of a postcard, so we can write:

(1/8)*y = x + 2 ...(Equation 1)

We also know that there are 15 postcards and 10 envelopes in the purchase, so the total cost of the postcards and envelopes is:

15x + 10[(1/8)*y] ...(Equation 2)

Finally, we have a notepad that costs "y" cents. So the total cost of the purchase is:

15x + 10[(1/8)*y] + y ...(Equation 3)

We are given that the total cost of the purchase is 1 dollar and 68 cents, which is equal to 168 cents. So we can write:

15x + 10[(1/8)*y] + y = 168 ...(Equation 4)

Now we have four equations (Equation 1, Equation 2, Equation 3, and Equation 4) with three variables (x, y, and 168). We can solve for x and y by using a system of equations.

From Equation 1, we can solve for y in terms of x:

(1/8)*y = x + 2

y = 8x + 16

Substituting this expression for y into Equations 2 and 3, we get:

15x + 10[(1/8)*y] = 15x + 10(8x + 16) = 160x + 160

15x + 10[(1/8)*y] + y = 15x + 8x + 16 = 23x + 16

Substituting these expressions into Equation 4, we get:

23x + 16 = 168

Solving for x, we get:

x = 6

Substituting this value for x into Equation 1, we can solve for y:

(1/8)*y = x + 2 = 6 + 2 = 8

y = 64

So the price of a postcard is 6 cents, the price of an envelope is (1/8)*64 + 2 = 10 cents, and the price of a notepad is 64 cents

User Urig
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