Linear Models: Banking

Let $a$ denote the first amount of money that Henry has deposited.

And let $d$ denote the amount of money Henry deposited on a weekly basis.

On the sixth week, Henry has deposited an additional 5 times, so $a + 5d = 70$ .

On the tenth week, Henry has deposited an additional 9 times, so $a + 9d = 82$ .

Subtracting the second equation from the first equation, we have $(a+9d) - (a+5d) = 82-70$ . Simplifying this gives $4d = 12$ or $d = 12\div4=3$ .

And thus, $a = 70 - 5d = 70 -5\cdot 3= 55$ .

Hence, the amount of money that Henry has in his bank account after $x$ weeks is $y = a + (x-1)d = 55 + (x-1) \cdot 3 = \boxed{3x + 52}.$