To solve this problem, let's break down each part.

Problem Analysis

Alonzo saves $6 per week. He has spent $90 of his savings and now has $48 left. We need to determine how many weeks he has been saving.

Let $w$ represent the number of weeks he has been saving.

Part (a): Setting up the Equation

Since he saves $6 per week, after $w$ weeks, he would have saved $6w$ dollars. After spending $90, he has $48 remaining, so we can write this as: $6w - 90 = 48$

The correct form is:

• Second Option: $6w - 90 = 48$

Part (b): Solving the Equation

Now, solve for $w$:

1. Start with the equation: $6w - 90 = 48$
2. Add 90 to both sides to isolate terms with $w$: $6w = 138$
3. Divide by 6: $w = 23$

Answer

Alonzo has been saving for 23 weeks.

Would you like further details or have any questions about this solution?

Here are five related questions to explore further:

1. What would the equation be if Alonzo saved $10 each week instead?
2. How much would Alonzo have after saving for 30 weeks if he spent $90?
3. How many weeks would Alonzo need to save to reach $200 after spending $90?
4. What is the total amount he saved if he hadn’t spent any money?
5. How would the answer change if Alonzo spent $60 instead of $90?

Tip: In word problems, translate each part of the scenario into mathematical terms to set up the equation accurately.