Problem Solving

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.

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:

Because the answer choices are in percentage form, there is another way to solve this question: we can use convenient numbers. Let's say the number of construction workers in 1992 is 100. We know, therefore, that the number of workers in 1996 is 1.2 × 100 = 120 workers.

We know that the unemployment rate among construction workers dropped from 16% on September 1, 1992 to 9% on September 1, 1996.

Thus we can say that the number of unemployed construction workers in 1992 is:

0.16 × 100 = 16

And the number of unemployed construction workers in 1996 is:

120 × 0.09 = 10.8 which is about 11.

We can now get the percent change:

[(New Value - Old Value)/(Old Value)] × 100

Using our values above the percent change formula will be:

[(11 - 16)/16] × 100

(-5/16) × 100

-5/16 is about -5/15, which reduces to -1/3. Again, -1/3 × 100 = -33.3%, which is closest to answer B

andymal wrote:Which way would you guys recommend? Scott's or Jeff's?

You asked a good question. Both approaches are great, so the best one is probably the one that makes the most sense to you. In your training, it might be a good idea to practice using both approaches. Discover for yourself which one takes less time and also yields consistently correct answers.