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.