At the beginning of the year, Abdoulaye had \( \$ 30 \) in savings and saved an additional \( \$ 14 \) each week thereafter. Lincoln started the year with \( \$ 60 \) and saved \( \$ 8 \) every week. Let \( A \) represent the amount of money Abdoulaye has saved \( t \) weeks after the beginning of the year and let \( L \) represent the amount of money Lincoln has saved \( t \) weeks after the beginning of the year. Write an equation for each situation, in terms of \( t \), and determine the number of weeks after the beginning of the year until Abdoulaye and Lincoln have the same amount of money saved.

Abdoulaye's savings can be expressed as the equation \( A = 30 + 14t \), where \( A \) is the total amount after \( t \) weeks. For Lincoln, the equation is \( L = 60 + 8t \). To find out when they will have the same amount saved, set the equations equal to each other: \[ 30 + 14t = 60 + 8t \] Now, solving for \( t \): 1. Subtract \( 8t \) from both sides: \[ 30 + 6t = 60 \] 2. Subtract \( 30 \) from both sides: \[ 6t = 30 \] 3. Divide by \( 6 \): \[ t = 5 \] So, after \( 5 \) weeks, Abdoulaye and Lincoln will have the same amount of money saved! In real-world terms, this scenario reflects how different savings habits can affect financial growth over time. Abdoulaye's strategy of higher weekly savings gives him a significant edge despite starting with less money. His consistent saving rate helps build wealth faster than Lincoln, whose growth is steadier but slower, which is a valuable lesson in personal finance management! One common mistake when solving these types of equations is forgetting to align the terms properly or miscalculating when combining them. It’s crucial to clearly isolate the variable (in this case \( t \)) and ensure accuracy at each step. You can enhance accuracy by checking your work as you go, ensuring that both sides of the equation are equal before solving further!