John has $486 in his bank account. Each week, he takes out $18 to pay for guitar lessons. Write an equation for this situation.

Question

 i need a equation for this problem and then i need to make a table of values, i also need to know which month he will run out of money

Answer 1

Let y = the amount of money left in John's bank account

Let x = the number of the week

y = 486 - 18x

 

     x          y     

     1        468      y = 486 - 18 =  468

     2        450      y = 486 - 18(2) = 450

     3        432      y = 486 - 18(3) = 432

    etc.

 

To find out when John will run out of money, let y = 0 and solve for x.

0 = 486 - 18x

-486 = -18x

27 weeks = x

 

Answer 2

Alright, Blake, don't make this too hard.

 

If I spend $18 a week, I spend 2(18) = 36 in 2 weeks, etc, right? Let's let w = the number of weeks.

 

If I start with 486, I have 486 - 18 after 1 month, 486 - 18(2) after 2 months, etc.

 

Since we have unknown months and are calling that number w (oh, let's call his bank balance b)...

 

b(w) = 486 - 18w

 

b(4) = 486 - 18(4) = 486 - 72 = 412, so after 4 weeks, he has $412 in the bank.

 

When he runs out of money, b(w) = 0.

 

0 = 486 - 18w

-18w = -486

-18w/-18 = 486/-18

w = 27 weeks

 

Let's check.

 

b(27) = 486 - 18(27) = 486 - 486 = 0

 

Boom.

Answer 3

w represents the number of weeks

 

486 - 18w

 

No substitute consecutive values (1, 2, 3, ..) to determine each week (that's the table)

When you get to zero, that's when the money is all gone!