Holiday Shopping and Video Games

Algebra Level 2

Deal City is having a sale on a video game that, because of its popularity, is notoriously hard to get a hold of. While waiting in line for Deal City to open (and the sale to begin), James notices that his friend Carlos is ahead of him and that there are only 5 5 people ahead of Carlos . If there is a total of 38 38 people in line, and 15 15 of those people are behind James . How many people are in line between James and Carlos ?

Source: MathCounts

10 10 23 23 15 15 6 6 9 9 16 16 8 8 5 5

Infinity Mathematics by Infinity Mathematics , 16, USA

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1 solution

Since James and Carlos are two of the people in line, there are 38 − 2 = 36 38 - 2 = 36 people in line with James and Carlos. That means the number of people ahead of Carlos, the number of people between Carlos and James, and the number of people behind James is 36 people. Thus, letting x x equal the number of people between Carlos and James, we can say that (since 5 5 people are ahead of Carlos and James is ahead of 15 15 people) 5 + x + 15 = 36 → x = 16 5 + x + 15 = 36 \rightarrow \boxed{x = 16} people.

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