define the variable for this situation

Question

jasmine and her sister are saying to buy MP3 players. jasmine has $50 and plans to save $10 per week. her sister has $80 and plans to save $7 per week. in how many weeks will jasmine have more money saved than her sister?

Answer 1

We can easily determine at which point they will have equal amounts

 

50 + 10X = 80 + 7X  where X ia the number of weeks

 

3X = 30

x = 10

 

In ten weeks they each have $150.

 

50 +10 x 10 = 150

80  7 x 10 = 150

 

So in the 11th week Jasmine will have more savings than her sister.

 

 

Answer 2

50+10x>80+7x, x=# of weeks

3x>30

x>10 weeks

Jasmine will have more than her sister after 10 weeks

Answer 3

Let W be the number of weeks.  Then, at the end of any given week, Jasmine has 50+10W and her sister has 80+7W.  To find when they'll have the same amount, we just set these equal:

 

50 + 10W = 80 + 7W

3W = 30

W = 10

 

As for interpretation and answering the original question, note that they'll have the same amount at the end of the 10th week, so the end of the 11th week will be the first time Jasmine has more than her sister.

 

If you have additional questions on how to solve these, feel free to let me know.