Question

Adele went to the post office to buy stamps and postcards. She bought a total of 25 stamps, some 39-cent stamps and the rest 23-cent postcards. If she paid $8.47 altogether, how many 39-cent stamps did she buy?

Answer 1

She bough 17 39-cent stamps and 8 23-cent postcards.

Explanation:

It is sometimes easier when dealing with problems like this to convert the money amount into cents, to avoid working with decimals. $8.47 equals 847 cents, which is what we can use for this problem.

Let's assume the following variables for the problem:

`{(x,"Number of 39-cent stamps"), (y, "Number of 23-cent postcards") :}`

Since we're told that 25 items (stamps?) were bought in total, we get the following equation:

`x + y = 25color(white)("aaaaaaaaaaaa")[A]`

We also know that 847 cents was spent altogether. If there were `x` 39-cent stamps bought, then the cost of those stamps was `39*x` cents. If there were `y` 23-cent postcards bought, then the cost of those postcards was `23*y`. Putting it together:

`39x + 23y = 847color(white)("aaaaaaa")[B]`

We have two variables, but two equations, so we have everything we need to finish the problem. In equation [A] we can solve for `x`:

`y = 25 - x`

We can now substitute this expression for `y` into equation [B] and solve for `x`:

`39x + 23y = 847`

`39x + 23(25 - x) = 847`

`39x + 575 - 23x = 847`

`16x + 575 = 847`

`16x = 272`

`x = 17 :. y = 8`

She bough 17 39-cent stamps and 8 23-cent postcards.

Answer 2

Adele bought `17` of the `39`-cent stamps.

Explanation:

This is a system of equations question. Let's first define our variables.

Let `x` be the number of `23`-cent stamps and `y` be the number of `39`-cent stamps.

We know that the total number of stamps is `25`. Thus:

`x+y=25`

We also know the total cost of the stamps is `8.47` (for the sake of the question, I'll drop the `$` sign).

Since we have `x` `23`-cent stamps, the total cost of these stamps is `.23x`. Similarly, we have `y` `39`-cent stamps, totaling `.39y` in cost. Put in an equation:

`.23x+.39y=8.47`

Now that we have two equations, we can simply solve.

First, I'll multiply the second equation by `100` to get rid of the decimals.

`23x+39y=847`

Next, I'll multiply the first equation by `23` to be able to cancel out the `x` terms since we're looking for `y` in the question.

`23x+23y=575`

Subtracting the second equation from the first equation, we get:

`16y=272`

`y=17`

Thus, Adele bought `17` of the `39`-cent stamps.