algebra word equation

Question

the pay for a mathematics major graduating from college is given by the formula P=43,800+2950t were t represents years worked after colleg. how many years would a mathematic major expect to work to be erning at least $90,000 per year? round to 1 decimal place

Answer 1

 

Set up as an inequality so the pay is at least as much as $90,000

 

43,800 + 2950*T  >=  90,000      

 

Now just solve for T.  first subt 43,800 from each side

 

2,950*T  >=  90,000 - 43,800    OR    2,950*T  >=  46,200

 

divide both sides by 2,950

 

T  >=  46,200/2,950    OR   T >= 15.661  or rounded to T >= 15.7  Years

 

 

===========================  ANSWER TO YOUR FOLLOWUP QUESTION LATE LAST NIGHT

 

Just noticed your additional question.

OK, the earlier problem had the math pay =

$43,800 + $2,920*T

 

Now, the gov't pay =

$40,700 + $3,150*T

So, in words its like if you are a math worker you start out making $43,800/ yr but each year get a pay raise of $2,920
the gov't worker starts out lower, at $40,700 but gets a higher raise each year of $3,150. **

Mathematically these are 2 lines (T is your X axis, Pay on the Y axis) but with different slopes (raise per year is different). Setting the equations =, we just solve for T where the lines intersect (representing = pay at that point). After that time T, the steeper slope (higher raise per year) will increasingly exceed the lower slope.

So just set each equation = to each other, and solve for T.


43,800 + 2,920*T = 40,700 + 3,150*T

 

(combine like terms, so we'll subtract 2,920*T from each side so T term is on rt)

43,800 + 0 = 40,700 + 3,150*T - 2,920*T     OR
43,800 = 40,700 + 230*T

 

Now, subtract 40,700 from each side to get the constant on the left side

3,100 = 230*T    

 

Now, divide by 230 to get T by itself on rt. side

 

3,100/230 = T

So, T = 13.478 YRS or rounding to 1 decimal number T = 13.5 Years

check our answer in our original equations using our answer,

T = 13.478 (years)

math worker:
43,800 + 2,920*T so

43,800 + 2,920*(13.478) = $83, 156.00 (rnd to nearest dollar)

Govt worker:
40,700 + 3,150*T so

40,700 + 3,150*(13.478) = $83, 156.00 (rnd to nearest dollar)

 

They are both equal, so it checks.



** (note: this is sometimes a real life scenario, where you start out in a profession at a lower initial pay, but it is expected to get higher raises, than some other position where you initially make more at first, but raises aren't as high)