How Much Fabric?
Six types of fabric were discontinued at a store. The fabric left on each roll was:
30 meters
32 meters
36 meters
38 meters
40 meters
62 meters
The discontinued fabric was put on sale at half price. Two rolls sold the first day. On the second day of the sale, 3 more sold. The total length of fabric on the 3 rolls sold the second day, was twice the total length of the 2 rolls sold the first day.
One roll of half price fabric remained ....
How much fabric was on the last roll?
30 meters
32 meters
36 meters
38 meters
40 meters
62 meters
The discontinued fabric was put on sale at half price. Two rolls sold the first day. On the second day of the sale, 3 more sold. The total length of fabric on the 3 rolls sold the second day, was twice the total length of the 2 rolls sold the first day.
One roll of half price fabric remained ....
How much fabric was on the last roll?
posted by Zaux at
9:18 AM
6 Comments:
unsold roll 40m
rolls sold day 1 = a & b
rolls sold day 2 = c & d & e
c+d+e = 2a+2b
if a,b= lowest values
c+d+e=124
if c,d,e highest values
c+d+e=140
thus c+d+e= between 124-140
this range can only be reached if one of c,d,e is 62
say e=62
then c+d= between 62-140
then the algebra ran out and used simple elimination!
regards, Curtis
Hi Curtis ...
good job ... the remaining roll is indeed the 40 m roll
Good man Curtis. I'm always disappointed when it can't (sensibly) be done algebraically all the way.
This post has been removed by the author.
This post has been removed by the author.
The total length is 30+32+36+38+40+62 = 238
label the 6 rolls: a,b,c,d,e,f (but don't know which is which)
Now consider:
238-f = a+b+c+d+e = (a+b)+(c+d+e) = (a+b)+2(a+b) = 3(a+b)
So require 238-f = 0 (mod 3) => 238 = 1 = f (mod 3)
In order {30,32,36,38,40,62} = {0,2,0,2,1,2} (mod 3)
So f must be 40 if the problem has a solution.
Post a Comment
Links to this post:
Create a Link
<< Home