Colin starts with $8.50 in his bank account and saves $15.75 each week. James starts with $7.50 in his bank account and saves $15.75 each week. Will the two boys ever have the same amount in their savings accounts?

They will never have the same value on their savings accounts.

Step-by-step explanation:

In this case since Colin and James started with different values on their accounts and they save money at the same rate, they'll never have the same amount. This can be show in a mathematical form. For that we will express the money on their account through an equation, where "x" is the amount of money they have and "t" is the number of weeks that pass by.

For Colin we have:

x = 8.5 + 15.75*t

For James we have:

x = 7.5 + 15.75*t

In order for them to have the same money, the equations must be equal, so:

8.5 + 15.75*t = 7.5 + 15.75*t

15.75*t - 15.75*t = 7.5 - 8.5

0 = - 1.5

Which is not a valid equation and therefore they'll never have the same savings on their accounts.