Amir has $100 and is saving $5 per week to buy a new DVD player. Pete has $80 and ius saving $7 per week to buy the same DVD player. Which system of equations can be used to find w, the number of weeks it would take them to have m, the money needed to buy the DVD player?
Obviously for Amir m = 100 + 5w
and for Pete m = 80 + 7w
They buy the same DVD player ----> m = m
clearly 80 + 7w = 100 + 5w etc
Yes, you are correct. The system of equations that can be used to find the number of weeks it would take Amir and Pete to have enough money to buy the DVD player can be represented as:
For Amir: m = 100 + 5w
For Pete: m = 80 + 7w
Since they are both saving money at a constant rate each week towards the same goal of buying the DVD player, the amount of money they have (m) will be equal. Therefore, we can equate the two equations as:
100 + 5w = 80 + 7w
Simplifying this equation will allow us to solve for the variable w, which represents the number of weeks it would take for them to have enough money to buy the DVD player.