Chapter 1.1, Problem 35PPSE

Solution

To write a model representing the total number of cards in Jay’s collection after $n$ months.

The model representing the total number of cards in Jay’s collection after $n$ months:

  $10+n$ .

Given:

Given that Jay owns $10$ cards and that he has decided to purchase a new card, for his collection, each month.

Calculation:

Since it is given that Jay owns $10$ cards, the number pattern representing the total number of cards starts with $10$ .

During the first month, he buys a card and then his collection has $10+1$ cards.

Now, he buys another card, during the second month, and then his collection has $\left(10+1\right)+1=10+2$ cards.

Proceeding in a similar way, it may be observed that, the total number of cards in Jay’s collection follows the rule $10+n$ , where $n$ represents the number of months after which Jay began his collection.

Thus, the mathematical model representing the total number of cards in Jay’s collection after $n$ months:

  $10+n$ .

Conclusion:

The model representing the total number of cards in Jay’s collection after $n$ months:

  $10+n$ .