SOLUTION: This is my grandson's other problem from his summer worksheet that he doesn't know how to do. Write a series of five decimal numbers that increase by 0.2 and add up to a total of 5

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Question 208667: This is my grandson's other problem from his summer worksheet that he doesn't know how to do. Write a series of five decimal numbers that increase by 0.2 and add up to a total of 5. I think I've figured it out just by guessing (.60+.80+1.00+1.20+1.40) but I have no idea how to explain to him the right way to figure this out. There must be a logical solution other than trial and error or guessing.
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
This is my grandson's other problem from his summer worksheet that he doesn't know how to do. Write a series of five decimal numbers that increase by 0.2 and add up to a total of 5. I think I've figured it out just by guessing (.60+.80+1.00+1.20+1.40) but I have no idea how to explain to him the right way to figure this out. There must be a logical solution other than trial and error or guessing.
.
Let x = first of five decimal numbers
then
x+.2 = second
x+.4 = third
x+.6 = fourth
x+.8 = fifth
.
x + (x+0.2) + (x+0.4) + (x+0.6) + (x+0.8) = 5
Grouping like-terms:
(x+x+x+x+x) + (0.2+0.4+0.6+0.8) = 5
5x + 2 = 5
5x = 5-2
5x = 3
x = 3/5
x = 0.6 (first decimal number)
.
The five numbers are indeed:
.6, .8, 1, 1.2 and 1.4