Question

Samara and Tony are saving money. Samara starts with 100 and saves 5 per week. Tony starts with 20 and saves 15 per week. After how many weeks would they have the same amount of money?

Answer 1

After using algebra to set up and solve the equations representing Samara's and Tony's savings over time, we find that they will have the same amount of money after 8 weeks.

Step-by-step explanation:

The student's question relates to finding out after how many weeks Samara and Tony will have the same amount of money given their individual starting amounts and weekly savings rates.

To solve this, let's use the equation of a line y = mx + b where y is the total amount of money saved, m is the rate at which they save money per week, x is the number of weeks, and b is the starting amount of money. For Samara, the equation would be y = 5x + 100, and for Tony, it would be y = 15x + 20.

To find out when they will have the same amount of money (i.e., when the two equations equal each other), we set them equal to each other and solve for x:
5x + 100 = 15x + 20.

Subtract 5x from both sides:
100 = 10x + 20.

Subtract 20 from both sides:
80 = 10x.

Finally, divide both sides by 10:
x = 8.

Therefore, after 8 weeks, Samara and Tony will have the same amount of money saved.