SOLUTION: johnny has a postcard collection 1/2 are from canada 1/4 are from japan 1/8 from france 1/6 from mexico 4 are from italy How many postcards does johnny have altogether

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: johnny has a postcard collection 1/2 are from canada 1/4 are from japan 1/8 from france 1/6 from mexico 4 are from italy How many postcards does johnny have altogether      Log On


   



Question 353891: johnny has a postcard collection
1/2 are from canada
1/4 are from japan
1/8 from france
1/6 from mexico
4 are from italy
How many postcards does johnny have altogether

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
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%281%2F2%29N%22%22%2B%22%22expr%281%2F5%29N%22%22%2B%22%22expr%281%2F7%29N%22%22%2B%22%22expr%281%2F10%29N%22%22%2B%22%224%22%22=%22%22N

The LCD of all those denominators is 70 so we multiply every term by red%2870%2F1%29


red%2870%2F1%29%22%22%2A%22%22expr%281%2F2%29N%22%22%2B%22%22red%2870%2F1%29%22%22%2A%22%22expr%281%2F5%29N%22%22%2B%22%22red%2870%2F1%29%22%22%2A%22%22expr%281%2F7%29N%22%22%2B%22%22red%2870%2F1%29%22%22%2A%22%22expr%281%2F10%29N%22%22%2B%22%22red%2870%2F1%29%22%22%2A%22%224%22%22=%22%22red%2870%2F1%29%22%22%2A%22%22N

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

35N%22%22%2B%22%2214N%22%22%2B%22%2210N%22%22%2B%22%227N%22%22%2B%22%22280%22%22=%22%2270N

Combine all the like terms on the left:

66N%22%22%2B%22%22280%22%22=%22%2270N

Subtracting 66N from both sides:

280%22%22=%22%224N

Dividing both sides by 4

70%22%22=%22%22N

So you have 70 post cards.

Edwin