umasarath52 wrote:In Country C, the unemployment rate among construction workers dropped from 16 percent on September 1, 1992, to 9 percent on September 1, 1996. If the number of construction workers was 20 percent greater on September 1, 1996, than on September 1, 1992, what was the approximate percent change in the number of unemployed construction workers over this period?
(A) 50% decrease
(B) 30% decrease
(C) 15% decrease
(D) 30% increase
(E) 55% increase
OG: 114
Answer B
Please help to explain..!!
Solution:
We are given two pieces of information that can be translated into equations. However, before we make those equations let's set up some variables as well to display some of the information provided.
16% = unemployment rate on September 1, 1992
9% = unemployment rate on September 1, 1996
c = number of construction workers on September 1, 1992
d = number of construction workers on September 1, 1996
Thus, we know:
0.16 × c = number of unemployed construction workers on September 1, 1992
0.09 × d = number of unemployed construction workers on September 1, 1996
We are asked to determine the approximate percent change in the number of unemployed construction workers over this period.
The formula for percent change is:
[(New Value - Old Value)/(Old Value)] x 100
Using our variables above, the percent change formula will be:
(0.09d - 0.16c)/(0.16c) × 100
In order to solve this formula we need to create an equation. We are given that the number of construction workers was 20% greater on September 1, 1996 than on September 1, 1992. Thus, we can say:
d = c + 0.2c = 1.2c
We can now substitute 1.2c for d in our percent change equation:
[(0.09 × 1.2c - 0.16c)/(0.16c)] × 100
[(0.108c - 0.16c)/(0.16c)] × 100
[(108c - 160c)/(160c)] × 100
[(-52c)/(160c)] × 100
(-13/40) × 100
Since we are asked to approximate we can change -13/40 to -13/39, which reduces to -1/3. We now have:
-1/3 × 100 = -33.3%
The closest answer to this is
B, a 30% decrease.
