Shane and Jay have a collection of postcards. Shane found 11 out of every 13 postcards in the collection. Jay found 45 fewer postcards than Shane. How many postcards are in their collection?
To find the total number of postcards in their collection, we need to determine the number of postcards Shane found and the number of postcards Jay found. Let's start by finding the number of postcards Shane found.
Shane found 11 out of every 13 postcards in the collection. This means that for every 13 postcards, Shane found 11. We can represent this relationship with the ratio 11/13.
To find how many sets of 13 postcards Shane found, we divide the total number of postcards Shane found by the number of postcards in each set: 11 ÷ 13 = 0.846.
Since we can't have a fraction of a set, we round this number down to the nearest whole number, which is 0. This means Shane found 0 complete sets of 13 postcards.
To find the number of postcards in these complete sets, we multiply the number of sets by the number of postcards in each set: 0 sets × 13 postcards = 0 postcards.
Next, we need to find the remaining postcards that Shane found. To do this, we multiply the remainder from the previous step (0) by the number of postcards in each set: 0 × 13 = 0 postcards.
Therefore, Shane found a total of 0 + 0 = 0 postcards.
Now let's find the number of postcards Jay found.
Jay found 45 fewer postcards than Shane. Since Shane found 0 postcards, we subtract 45 from 0: 0 - 45 = -45 postcards.
Since we can't have a negative number of postcards, we conclude that Jay found 0 postcards as well.
To find the total number of postcards in their collection, we add the number of postcards Shane found to the number of postcards Jay found: 0 + 0 = 0.
Therefore, the total number of postcards in their collection is 0.