SOLUTION: Hi- I teach Adult Basic Education, mostly I help students pass the GED test. I am no Mathematician, and sometimes I get a question that I can not explain the Mathematics behind sol

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Question 337092: Hi- I teach Adult Basic Education, mostly I help students pass the GED test. I am no Mathematician, and sometimes I get a question that I can not explain the Mathematics behind solving. This is an example of one such problems.
James Torres works in an electircal equiptment factory and does the final assembly on power trasfer units. He keeps a log of the number of units he completes each day. He works five days a week. Below is his log for the week of October 2 through October 6.
Production Log
Name: James Torres
Week: 10/2-10/6
Date No. units Assembled
10/2 12
10/3 15
10/4 18
10/5 17
10/6 16
Weekly total ______
Daily average ______

Here is the question:
The total for 10/3 is how much higher than the total for 10/2?
a. 3%
b. 12.5%
c. 20%
d. 25%

The answer is d. 25%.. . but WHY? The only rational I can come up with is 3 is the difference of 15 and 12, and 3 is 25% of 12. But why do I do that to solve this problem? How do I explain this to my students? Most of my students are visual learners so anything I can do to help me understand this, will in turn help them..
Thanks so much for taking the time to explain this to me, I really appreciate it.
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Whenever you're looking at percentage changes, you take the difference between old and new value and then divide it by the old value.
So then, the percentage change for those two days would be
C=%2815-12%29%2F12=3%2F12=25%
Positive 25% so you know the number increased.
In other words, the change from old to new value is 25% of the old value.
12%2B%2825%2F100%2912=12%2B%281%2F4%29%2812%29=12%2B3=15
.
.
.
As another example, if it was reversed say 15 today and 12 tomorrow. Then the percentage change would be
C=%2812-15%29%2F15=-3%2F15=-20%
Negative 20%, so you know the number decreased.
15%2B%28-20%2F100%29%2815%29=15%2B%28-1%2F5%29%2815%29=15-3=12
.
.
.
So the percentage change going from 12 to 15 is not the same magnitude as going from 15 to 12 because it's a percentage of the starting (old) value.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
10/2 12
10/3 15
10/4 18
10/5 17
10/6 16
Weekly total ______
Daily average ______
Here is the question:
The total for 10/3 is how much higher than the total for 10/2?
a. 3%
b. 12.5%
c. 20%
d. 25%
The answer is d. 25%.. . but WHY? The only rational I can come up with is 3 is the difference of 15 and 12, and 3 is 25% of 12. But why do I do that to solve this problem? How do I explain this to my students? Most of my students are visual learners so anything I can do to help me understand this, will in turn help them..
Thanks so much for taking the time to explain this to me, I really appreciate it.
-------------
Right.
The quantitative gain from 10/2 to 10/3 is 15-12.
That is a gain of 3 from a base of 12
So the percent gain is figured from a base of 12.
You could set up an equation to figure the percent (per one-hundred)
gain as follows:
x/100 = 3/12
x = 100(3/12)
x = 100(1/4)
x = 25
The percent gain is 25%.
============================
Visualizing this gain with blocks might also be a help.
Compare 12 blocks to 15 blocks to see the gain.
---
Keep duplicating the 12 to 15 picture till you have x to 100
The x will be seen to be 25.
=====================
Cheers,
Stan H.