We will write equations for both Blake and Noah based on their savings pattern.

Step 1: Write Equations

• Blake started with $55 and saves $7 per week.
  So, his savings equation is:
  $B = 55 + 7t$
• Noah started with $35 and saves $12 per week.
  His savings equation is:
  $N = 35 + 12t$

Step 2: Find When Blake and Noah Have the Same Amount of Money

To determine when they have the same savings, set their equations equal to each other:

$55 + 7t = 35 + 12t$

Step 3: Solve for $t$

1. Subtract $7t$ from both sides: $55 = 35 + 5t$
2. Subtract 35 from both sides: $20 = 5t$
3. Divide by 5: $t = 4$

Step 4: Determine the Amount of Money Saved

Substituting $t = 4$ into either equation:

For Blake: $B = 55 + 7(4) = 55 + 28 = 83$

For Noah: $N = 35 + 12(4) = 35 + 48 = 83$

Final Answer:

Blake and Noah have saved $83 after 4 weeks.

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Would you like a step-by-step breakdown for further clarity?

Here are five related questions for practice:

1. If Blake continues saving at the same rate, how much will he have after 10 weeks?
2. If Noah saves for 15 weeks, how much will he have in total?
3. If Blake increases his weekly savings to $10 per week, when will he and Noah have the same savings again?
4. How much more money does Noah have than Blake after 6 weeks?
5. If both continue saving indefinitely, who will have more money after 20 weeks and by how much?

💡 Tip: Always set up an equation with variables to compare different scenarios systematically!