Question 353891
<pre>
The fractions you gave will not yield a solution because they
add to more than 1 whole set of post cards by themselves. Perhaps
you mis-typed one of them. So I substituted some other fractions that 
will give an answer:

1/2 are from Canada
1/5 are from Japan
1/7 from France
1/10 from Mexico
4 are from Italy

Let N = the number of postcards altogether
{{{expr(1/2)N}}}{{{""+""}}}{{{expr(1/5)N}}}{{{""+""}}}{{{expr(1/7)N}}}{{{""+""}}}{{{expr(1/10)N}}}{{{""+""}}}{{{4}}}{{{""=""}}}{{{N}}}

The LCD of all those denominators is 70 so we multiply every term by {{{red(70/1)}}}


{{{red(70/1)}}}{{{""*""}}}{{{expr(1/2)N}}}{{{""+""}}}{{{red(70/1)}}}{{{""*""}}}{{{expr(1/5)N}}}{{{""+""}}}{{{red(70/1)}}}{{{""*""}}}{{{expr(1/7)N}}}{{{""+""}}}{{{red(70/1)}}}{{{""*""}}}{{{expr(1/10)N}}}{{{""+""}}}{{{red(70/1)}}}{{{""*""}}}{{{4}}}{{{""=""}}}{{{red(70/1)}}}{{{""*""}}}{{{N}}}

Then you will not have any fractions when you multiply all those

{{{35N}}}{{{""+""}}}{{{14N}}}{{{""+""}}}{{{10N}}}{{{""+""}}}{{{7N}}}{{{""+""}}}{{{280}}}{{{""=""}}}{{{70N}}}

Combine all the like terms on the left:

{{{66N}}}{{{""+""}}}{{{280}}}{{{""=""}}}{{{70N}}}

Subtracting {{{66N}}} from both sides:

{{{280}}}{{{""=""}}}{{{4N}}}

Dividing both sides by 4

{{{70}}}{{{""=""}}}{{{N}}}

So you have 70 post cards.

Edwin</pre>