SOLUTION: Please help me with this story problem. A post office sells first-class stamps and postcard stamps. For the year, the post office sold 7 first -class stamps for every 2 postcard

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Question 78342: Please help me with this story problem.
A post office sells first-class stamps and postcard stamps. For the year, the post office sold 7 first -class stamps for every 2 postcard stamps sold.

a. the post office sold 46, 260 stamps for the year. How many of them were first-class stamps? how many were postcard stamps?
Found 2 solutions by bucky, amalm06:
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Since the post office sells 7 first-class stamps for every 2 postcard stamps, this means
that of every 9 stamps it sells, 7 are first-class.
.
Therefore the ratio of first-class stamps to total stamps is 7 to 9 or 7:9. You are told
that the total of the stamps sold in a year is 46,260. With these figures we can now write
a proportion:
.
7%2F9+=+x%2F46260
.
in which x represents the number of first-class stamps sold in a year.
.
You can begin to solve proportions by cross-multiplying ... that is by multiplying the numerator
of the left side times the denominator of the right side, multiplying the denominator
of the left side times the numerator of the right side, and then setting the two products
equal.
.
These two multiplications are: 7*46260 and 9*x. Setting them equal results in:
.
9x+=+7%2846260%29
.
Performing the multiplication on the right results in:
.
9x+=+323820
.
Finally divide both sides by 9 to solve for x. This is:
.
x+=+323820%2F9+=+35980
.
So you know that 35980 of the 46260 stamps were first-class. Subtract 35980 from the
46260 and you get that the number of postcard stamps sold in the year was:
.
46260+-+35980+=+10280
.
You can check this to see if the ratio of first-class stamps to postcard stamps is 7:2.
In other words, does:
.
35980%2F10280
.
give you the same ratio as 7%2F2
.
Dividing 35980 by 10280 results in 3.5. And dividing 7 by 2 also results in 3.5.
The answer checks!
.
Hope this gives you some insight into solving proportions.

Answer by amalm06(224) About Me  (Show Source):
You can put this solution on YOUR website!
Let F = first-class stamps, P = postcard stamps
Then F/P = 7/2
This means that for every 9 stamps, 7 are first-class stamps
If 46260 stamps are sold, then F=(7/9)(46260)=35980 first-class stamps (Answer)
And 46260-35980=10280 postcard stamps (Answer)