Question

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?

Answer 1

58

Explanation:

Let t and m represent the numbers of cards had by Tom and Max, respectively. Then the problem statement tells us ...

• t + m = 72
• 4m +2 = t

We want to solve for t. If we multiply the first equation by 4 and subtract the second, we get ...

... 4(t +m) -(4m +2) = 4(72) -(t)

... 4t +4m -4m -2 = 288 -t . . . . . . . eliminate parentheses

... 5t = 290 . . . . . . . . . . . . . . . . . . . add t+2, collect terms

... t = 58 . . . . . . . . divide by the coefficient of t

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Alternate Solution

You can work this in your head if you realize that subtacting 2 from the total means that Max has 1/5 of the new amount. 1/5 of 70 is 14, so Tom has 72 - 14 = 58 cards.