Alright, let's break this problem down step by step.
1. Understand the Problem: We know you start with $80 in your bank account. Each week, you're adding $9 from your allowance and $15 from your paycheck. The equation provided, b = 80 + (15 + 9)w, tells us how much money, b, you have in your account after w weeks.
2. Translate to an Equation: We want to find out how many weeks (w) it will take for your bank account to have $175. So, we can set b equal to 175 and solve for w:
175 = 80 + (15 + 9)w
3. Simplify the Equation: First, let’s simplify the equation. 15 + 9 equals 24. So, the equation becomes:
175 = 80 + 24w
4. Solve for w: Now let's get w by itself. First, we will get rid of the 80 that's being added to the 24w. We can do this by subtracting 80 from both sides:
175 - 80 = 80 + 24w - 80
95 = 24w
Now, we need to isolate w. Since 24 is being multiplied by w, we can do the opposite to get rid of it, which is dividing. Let's divide both sides by 24:
95/24 = 24w/24
w ≈ 3.96
5. Interpret the Answer: We found that w is approximately 3.96. Since weeks are a measure of time, it doesn’t make sense to have a fraction of a week (we can't go 3.96 weeks into the future). We need to round up to the next whole number, which is 4, because even if you’re a tiny bit short at 3 weeks, you will definitely have $175 after 4 weeks.
So, the answer is that in 4 weeks from now, you will have at least $175 in your bank account. Great job working through this problem!