2015 AMC 8

Complete problem set with solutions and individual problem pages

Problem 9 Easy

On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working 20 days?

  • A.

    39

  • B.

    40

  • C.

    210

  • D.

    400

  • E.

    401

Answer:D

Solution 1

First, we have to find how many widgets she makes on Day 20. We can write the linear equation y=-1+2x to represent this situation. Then, we can plug in 20 for x: y=-1+2(20) -- y=-1+40 -- y=39. The sum of 1,3,5, \cdots 39 is \dfrac{(1 + 39)(20)}{2}= \boxed{\textbf{(D)}~400}.

 

Solution 2

The sum is just the first 20 odd counting/natural numbers, which is 20^2=\boxed{\textbf{(D)}~400}.

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