Solving Multi-Step Equasions

Question

You have $70 in your bank account. Each week you plan to deposit $9 from your allowance and $10 from your paycheck. The equation b = 70 + (10 +9)w gives you the amount b in your account after w weeks. How many weeks from now will you have $200 in your bank account?

Answer 1

b = 70 + (10 +9)w = 70 + 19w

 

We want to know the value of w when b = 200.  Set b = 200 in the equation and solve for w:

 

     200 = 70 +19w

 

Subtract 70 from both sides of the equation:

 

     130 = 19w

 

Can you finish it from here?

Answer 2

"The equation b = 70 + (10 +9)w gives you the amount b in your account after w weeks"

"How many weeks from now will you have $200 in your bank account?"  At this point, the balance, b, equals $200.  What is w?

 

    200 = 70 + (10+9)w

    130 = 19w               (subtract 70 from both sides)

     6.84 = w                 (divide both sides by 19)

 

This means that if you paid continuously (every minute of every day), then partway through the 6th week, the balance would exceed $200.  Since you only pay each week,

      !t the end of 6 weeks, the balance would be $184     (not there yet!)

      At the end of 7 weeks, the balance would be $203     (made it!)