#3 step by step (equations and variables)

Question

Sally's bank account has $650 in it. Every week, Sally withdraws $50 to pay for her dog sitter. What is the maximum number of weeks that Sally can withdraw the money so there is at least $75 remaining in the account? Write and solve an inequality to find the solution, and graph the solution on a number line

Answer 1

Let W be the number of weeks Sally has been withdrawing money.  The total in the account would be represented by 650-50W at any given time.

 

To remain over or equal to $75 the equation to solve is

 

650 - 50W >= 75

we need to get the variable on one side and the constants on the other so subtract 650 from each side...

-50W >= 75-650

-50W >= -575

Now we need to divide out the coefficient of the variable so divide both sides by -50.   Note that multiplying or dividing an inequality by a negative reverses the inequality so...

W <= (-575)/(-50)

W <= 11.5

 

So in whole numbers the maximum number of weeks Sally can remove $50 from the account and still have at least $75 is 11 weeks.

 

Check:  11(50) = 550 which if removed still leaves $100 in the account after 11 weeks which meets the criteria since 100>=75

 

12(50) = 600 which if removed only leaves $50 in the account which is less than the requisite $75 so 12 weeks is too long.