Sure! Let's break down the problem step-by-step to form the equation that represents Bob's savings.
1. Initial Amount:
- Bob starts with [tex]$150 in his savings account. This is a constant value that does not change over time.
2. Monthly Savings:
- Bob saves $[/tex]40 every month. This means that for every month [tex]\( x \)[/tex], Bob's savings will increase by [tex]$40.
To write an equation that represents Bob's total savings \( y \) over time, we need to combine these two pieces of information:
3. Equation Formation:
- The total savings \( y \) after \( x \) months will be the sum of the initial amount and the total savings accumulated over \( x \) months.
- The initial amount is $[/tex]150.
- The savings accumulated over [tex]\( x \)[/tex] months is $40 multiplied by the number of months, [tex]\( 40x \)[/tex].
Putting these together, we have:
[tex]\[ y = 40x + 150 \][/tex]
This equation represents Bob's savings over time, where [tex]\( x \)[/tex] is the number of months and [tex]\( y \)[/tex] is the total amount in his savings account.
