word problem

Question

Fourteen percent of the towns population are above the age of 65. If there are about 320 residents over the age of 65,what is the towns population?

Answer 1

14 percent of the population = 320 residents

 

There is a formula that will help with these situations:

^is/_of = ^{percent (%)}/_100.

 

In this case, we can rephrase the question to as:

320 residents is 14 percent of _____.

 

Substitute into the formula

 

³²⁰/_x = ¹⁴/₁₀₀

 

Cross multiply

14x = 32,000

x = 2,285

 

The population is 2,285 people

Answer 2

14 percent of the towns population can be rewritten as 14/100 ∗ Town's population = 320.  Then solve 14/100 P = 320.  Multiply both sides by the reciprocal of 14/100.  Multiply by 100/14.  So P = 320 * 100/14 = 32000/14=2285.71 or approximately 2286 people.  

Answer 3

This is one of those made-up math questions that does not present the full problem.

 

In particular, the 14% has already been rounded.  We know this because we do not get an integer answer for the number of people (just wait and see).

 

So, translate:

  "Fourteen percent of the towns population are above the age of 65. If there are about 320 ..."

       14/100             *              x                                                                         =   320

 

Note that "fourteen percent" may be written as 14/100 or 0.14 as needed by the problem.

       (14/100)x = 320

       x = (320)(100/14)        [multiply both sides by (100/14)]

       x = 32000/14

       x = 2285.714                [I said to look out for this!]

 

What do we do now?  Well, it is wrong to round to the nearest person (because the percent has already been rounded); even books and teachers and tutors miss this point.

 

If 14% has already been rounded to the nearest percent, then any number from 2207 to 2370 works.  For example, 14% (rounded) of 2300 is 320.      [that is, 320/2300 = 13.91%, rounded is 14%]

 

Now, the word "about" 320 makes this approximation a little better, but it is still not appropriate to round the calculation to the nearest whole person.  So, watch out!