Question

There are 12 baseball trading cards in 4 packages. each package has the same number of cards. Write a rule in words for the number of packages Justin needs to buy to get x cards. Then write the rule as an algebraic expression.

Answer 1

• Rule in words:

The number of packages Justin needs to buy to get x cards is x divided by 3.

• Rule as an algebraic expresssion:

`y=x/3`

Step-by-step explanation:

This is a direct variation problem.

Since each package has the same number of cards, the number of cards is proportional to the number of packages.

12 baseball cards in 4 packages means that there are 12/4 = 3 cards per package, so:

• The number of cards is 3 times the number of packages.

• The number of packages is the number of cards divided by the number of 3.

So, the rule in words for the number of packages Justin needs to buy x cards is one third of x. This table may help you to visualize it:

Number of packages: 1 2 3 4 5

Number of cards: 3 6 9 12 15

To find the algebraic expression that describes the same rule, you can set the following proportion:

`(12)/(4) =(x)/(y)`

Where y is the number of packages and x is the number of cards.

And from that you solve for y:

`(12)/(4) =(x)/(y)\\ \\ 12y=4x\\ \\ y=4x/12\\ \\ y=x/3`