need to turn a word problem into an equation and not sure how to go about it

Question

If you are paid a hourly wage of $9.00 determine an equation for finding your weekly gross pay (p) for t hours specify an amount between 25 and 40 hours worked for 1 week and determine your gross pay for that week. 

Answer 1

The key to solving a word (story) problem is to correctly translate the words and phrases into precise, concise math expressions (with variables and operations).  Also, the units of values will be important.

 

In this problem, there is a constant, $9.00 per hour, which is written as $9.00/hr.  The problem called this "an hourly wage," so you must supply the correct units.

 

There is an independent variable, t, for the number of hours worked and a dependent variable, p, for the pay that this produces.  Independent variables can change easily and, when they do, they make the dependent variable change.  In math, the dependent variable is "a function of" the independent variable.

 

Now, the units:  When dollars per hour (that is $/hr) are multiplied by hours (that is, hr), the hours cancel out, leaving only dollars (that is, $), which is the unit that we want for pay.  Thus, we would expect to see something like 9t in the equation.  For problems where there is a base pay plus a commission, the base pay must already be in dollars.  For problems where tips add to the pay earned, the tips must be in dollars.  All amounts must already be in dollars or be converted to dollars in order to add them correctly.

 

So, the equation is:

    Pay = (pay rate in dollars per hour)*(hours worked)

     p  = 9t             (note: numbers are usually written before variables when they are multiplied)

 

O.K., let's pick an easy value between 25 and 40 hours worked.  How about 28.5 (hey! that's not easy; well then, you do 30).

   p = 9t

   p = 9(28.5)

   p = $256.50    (either write units throughout or be sure to put units back on when done)

 

(Note: this pay actually has the units of dollars per that week because the problem asks, "determine your gross pay for that week.")

Answer 2

The equation will be 

G = 9t,  where G is the gross amount you earned and t is the number of hours you worked for that one week.

However, since there is an interval of time, 25 to 40 hours given, this is what you need to do,

9(25)≤ G ≤ 9(45)

the gross amount will be between amount earned

for 25  hours work week and 40 hours work week.

225 ≤ G ≤ 405

The gross amount earned is between $225 and $405.

Answer 3

Hello,

 

If the hourly wage is $9.00, then this person makes $9.00 for each hour worked. Mathematically, this looks like p = 9*t (that is, for every t hours this person works, they get $9. So for example, is someone worked 2 hours, the equation would look like p = 9*2 and p would be equal to 18). For hours between 25 and 40, you would do the same thing but change the numbers. For example, if someone worked 30 hours, the equation would be p = 9*30 and p would be equal to 270.