A man had 432 watches. He sells 1 watch everyday. The algebraic expression to show that the number of watches he would be left with after 't' weeks is?

Break Down the Problem

1. Understanding the initial condition: The man starts with 432 watches.
2. Daily sales: He sells 1 watch every day.
3. Weekly sales: Calculate how many watches are sold in 't' weeks.

Relevant Concepts

1. Total watches sold in 't' weeks: Since there are 7 days in a week, in 't' weeks he will sell: $\text{Watches Sold} = 7 \times t$

2. Remaining watches formula: The remaining watches after 't' weeks will be the initial number of watches minus the number of watches sold.

Analysis and Detail

1. Calculate the remaining watches:

   • Initial watches: 432
   • Watches sold in 't' weeks: $7 \times t$

   Therefore, the expression for the remaining watches is: $\text{Remaining Watches} = 432 - (7 \cdot t)$

Verify and Summarize

• Check if the expression makes sense: If $t = 0$, remaining watches = 432, which is correct. If $t = 1$, remaining watches = 432 - 7 = 425, and so on.

Final Answer

The algebraic expression to show the number of watches he would be left with after 't' weeks is: $432 - 7t$