SOLUTION: Lina bought some origami papers to fold some paper cranes. On the first day, she used 3 more origami papers than 5/8 of the origami papers. On the second day, she used 3 more origa

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Lina bought some origami papers to fold some paper cranes. On the first day, she used 3 more origami papers than 5/8 of the origami papers. On the second day, she used 3 more origa      Log On


   

Question 1204318: Lina bought some origami papers to fold some paper cranes. On the first day, she used 3 more origami papers than 5/8 of the origami papers. On the second day, she used 3 more origami papers than 25% of the remaining origami papers. On the third day, she used the remaining 15 pieces of origami paper. How many pieces of origami papers did Lina use?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


To learn more about solving this kind of problem, let's work the problem both "forwards" and "backwards" and compare the two solutions.

(1) Working forwards....

Let the original number of papers be x

Number used on the first day: %285%2F8%29x%2B3
Number remaining after the first day: x+-+%28%285%2F8%29x%2B3%29+=+%283%2F8%29x-3

Number used on the second day: %281%2F4%29%28%283%2F8%29x-3%29%2B3
Number remaining after the second day:

The number remaining after the second day and used on the third day was 15:

%28%283%2F4%29%28%283%2F8%29x-3%29-3%29=15

%283%2F4%29%28%283%2F8%29x-3%29=18
%283%2F8%29x-3=%284%2F3%2918=24
%283%2F8%29x=27
x=%288%2F3%2927=8%2A9=72

ANSWER: 72

CHECK:
start: 72
used first day: (5/8)72+3 = 48
number left after first day: 72-48 = 24
number used second day: (1/4)24+3 = 6+3 = 9
number left after second day: 24-9 = 15

(2) working backwards....

number after second day: 15
number left before she used the "3 more" on the second day: 15+3 = 18
number left before she used 1/4 of what she had at the beginning of the second day, LEAVING HER WITH 3/4 of what she had at the beginning of that day: 18*(4/3)=24
number left before she used the "3 more" on the first day: 24+3 = 27
number left before she used 5/8 what she had at the beginning of the fist day, LEAVING HER WITH 3/8 of what she had at the beginning of that day: 27*(8/3)=9*8=72

ANSWER: 72

You see that working the problem forwards leads to rather complicated equations that need to be solved.

Working backwards, you are only doing arithmetic; but it takes practice to be able to correctly determine the exact arithmetic that needs to be performed at each stage.

So both methods have their disadvantages in this problem where papers are used on two successive days, and both methods are good.

But note that, if the problem was similar but papers were being used for three or four or five days (or more!), working the problem forwards would lead to extremely ugly equations; so for that kind of problem working backwards is sure to be less work.