We are going to use the variable x for representing the number of weeks.
Variable definition: Let x represents the number of weeks.
Left-side expression:
-308 + 17.6* x (Since each week she will deposit $17.6)
Right-side expression:
-80 + 8.1*x (Since each week she will deposit $8.1)
Write the equation:
-308 + 17.6* x = -80 + 8.1*x (Since they want to calculate when both values are equal)
Solve the equation:
-308 + 17.6* x + 80 = + 8.1*x (Adding 80 on both sides of the equation)
-228 + 17.6*x= 8.1*x (Subtracting like terms)
-228 = -17.6*x + 8.1*x ( Subtracting 17.6 on both sides of the equation)
-228 = -9.5*x (Subtracting like terms)
-228/(-9.5) = x ( Dividing by -9.5 on both sides of the equation)
24 = x
Answer: Both accounts have the same balance after 24 weeks.
Justify the solution:
Replacing x=24 in the left-side expression, we have:
-308 + 17.6*(24) = 114.4
Replacing x=24 in the right-side expression, we have:
-80 + 8.1*(24) = 114.4
We can see that both accounts have the same value after 24 weeks
Evaluate the reasonableness of the solution and the problem-solving process. Is the solution reasonable?Why or why not?
The solution is reasonable because after 24 weeks they have the same balance and it is not a huge number of weeks, in fact, time in months is equal to 6 months approximately.
Is the process effective? Why or why not?
It is an effective process because it is more practical than making a table and calculating the values week by week until finding the solution.