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?

2 Answers
Oct 13, 2017

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.

Oct 13, 2017

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.