Math CentralQuandaries & Queries


Question from Maureen, a student:

Together, Tom and Max have 72 football cards. Tom has 2 more than 4 times as many cards as Max has. How many football cards does Tom Have?

HI Maureen,

One of the keys to solving word problems is to carefully read the problem and attempt to convert it to an algebra problem. In this problem the important quantities are the numbers of cards that Tom and Max have so I would start giving these quantities algebraic symbols.

Let $t$ be the number of cards that Tom has and $m$ be the number of cards that Max has.

The first sentence in the problem says that the total number of cards is 72. Said algebraically this is

$t + m = 72.$

The second sentence says that if I multiply he number of cards that Max has by4 and then add 2 I get the number of cards that Tom has. Thus

$ t = 4m + 2.$

You have now converted the word problem into two algebraic equations. Can you solve the equations?


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