SOLUTION: Amy has $20 in her savings account and is adding $10 every week. Jim has $180 in his savings account but has to take out $30 every week. Write the equation that represents the amou

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Amy has $20 in her savings account and is adding $10 every week. Jim has $180 in his savings account but has to take out $30 every week. Write the equation that represents the amou      Log On


   

Question 1107664: Amy has $20 in her savings account and is adding $10 every week. Jim has $180 in his savings account but has to take out $30 every week. Write the equation that represents the amount that each has in their account. Don't forget to define your variable.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x equal the number of weeks.
let y = the amount of money that each has in their account.

the equation for amy will be y = 20 + 10 * x.

the equation for jim will be y = 180 - 30 * x.

the value of y for amy will be different than the value of y for jim except when the amount in each of their accounts is the same.

if you graphed both equations, you would see when this happens.

the graph of both their equations would look like this:

$$$

the blue line is amy's line.

the red line is jim's line.

they intersect at the coordinate point of (4,60).

the means that the value of x is 4 and the value of y is 60.

that means that they would both have the same amount of money in their account in 4 weeks, and that amount would be 60 dollars.

going to amy's equation, we get y = 20 + 10x.
when x = 4, the equation becomes y = 20 + 40 = 60.

going to jim's euation, we get y = 180 - 30x.
when x = 4, the equation becomes y = 180 - 120 = 60.

the value of y is the same at 60 which means they both have 60 dollars in their account after 4 weeks.

your solution is:

the equation for amy is y = 20 + 10x.

the equation for jim is y = 180 - 30x.

y represents the amount of money in their respective accounts.
x represents the number of weeks from their starting balance.

their current balance is when x = 0.