You begin with $25 in a savings account and $50 in the checking account. Each week you deposit $5 into savings and $10 into checking. After how many weeks is the amount in checking twice the amount in savings? write and solve an equation.

We start with 25 dollars and each week we deposit 5 dollars. So the function that would modelate the total amount of money in function to the weeks passed would be:

f(x) = 25 + 5x (first x = 0, f(x) would be 25; after one week x=1 the function would give us the value 25 + 5 = 30,...)

Now we need to find a function g(x) for the amount of savings in the checking account.

We start with 50 dollars and each week we deposit 10 dollars. Therefore, our function of the total amount saved in terms of how many weeks have passed is:

g(x) = 50 + 10x (for x = 0, g(x)=50, after 1 week we have x = 1, g(x)=50 + 10 = 60

Finally we're going to find after how many weeks will pass until the amount in checking is twice the amount in savings.
Notice that after 1 week, the amount in the savings account is

f(1) = 25 + 5(1) = 25 + 5 = 30

And the amount in the checking account after one week is:

g(1) = 50 +10(1) = 50 + 10 = 60

We can see that after one week, the amount in the checking account is twice the amount in savings.