Greg currently has 30 and receives a new one every 4 months. As a competition, Mark wants to start collecting ties as well. He buys a tie every month until he has the same amount as Greg. How many months until Mark has the same amount? How many ties are there? Hint: use one variable for “# of months” and one for “# of ties”.

9514 1404 393

  40 months

Step-by-step explanation:

Let t represent the number of months. Then Greg's tie count (g) will be ...

  g = 30 + t/4 . . . . . . average rate of tie accumulation is 1/4 tie per month

And Mark's time count (m) will be ...

  m = t . . . . . . . . . . . . average rate of tie accumulation is 1 per month

We want these numbers (g, m) to be equal:

  g = m

  30 +t/4 = t . . . . . substitute the equivalent expressions

  30 = 3/4t . . . . . . subtract t/4

  40 = t . . . . . . . . . multiply by 4/3

After 40 months, Mark and Greg will have the same amount of ties.

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