Question

A tree house costs $530. You plan to save $10 each week. Your parents will help pay $80 of the cost. Your savings plan can be modelled with the equation S=10w+80. After how many weeks will you be able to afford the tree house?

-47. -46. -45. -44.

Answer 1

Let's analyze and interpret the equation s = 10w + 80.
s is the total savings so far. In order to afford the tree house, s must equal $530.
10w represents saving $10 per week, with w being the number of weeks that have passed so far.
+ 80 this is the y-intercept, or starting point. This is the money that the parents gave.

Since we want $530 in savings, let's say s = 530. This way we can solve for w and find how many weeks it will take for s to get to equaling 530.

s = 10w + 80
s = 530
530 = 10w + 80

In this equation, we must isolate w. The first step in doing this is subtracting 80 from both sides.
530 - 80 = 450
10w + 80 - 80 = 10w
450 = 10w

Now we must dividing both sides by 10.
450 / 10 = 45
10w / 10 = w
45 = w

w = 45
This means it takes 45 weeks under this savings plan in order to save up $530.
So our final answer is 45 weeks.

Hope this helps!