Question 523331: My daughter (5th grade) has this homework problem. Although we found the answer the "hard" way, I wanted to know how to solve it with basic algebra, if possible. Thanks!
James has 75 pieces of candy. If he eats one piece today, two pieces tomorrow, three pieces the next day, and so on, how many days will it take him to eat all of his candy?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! James has 75 pieces of candy.
If he eats one piece today, two pieces tomorrow, three pieces the next day, and so on, how many days will it take him to eat all of his candy?
:
There is a quadratic equation for this, y = .5x^2 + .5x
where x = the number of the day and y is the total number of candies consumed up to and including that day.
:
For example on day 4:
y = .5(4^2) + .5(4)
y = .5(16) + 2
y = 10 candies
:
Find x when y = 75 candies
.5x^2 + .5x = 75
.5x^2 + .5x - 75 = 0
solve for x using the quadratic formula
the positive solution is not an integer
x = 11.76
so the all the candies will be consumed on day 12
:
If you want to know how this equation was derived, let me know in the comment.
But I don't think this is covered in 5th grade algebra
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