Final answer:
Darnell and Lance will have the same amount of money in 5 weeks, at which point they will both have $65. If both boys continue saving at this rate, Darnell will have $100 first.
Step-by-step explanation:
To find out when Darnell and Lance will have the same amount of money, we need to compare their savings each week. Darnell saves $5 each week, while Lance saves $8 each week. We can set up an equation to represent this:
Darnell's savings = Lance's savings
$40 + $5w = $25 + $8w
where w represents the number of weeks.
By solving this equation, we can find the value of w. Substituting the values:
$40 + $5w = $25 + $8w
$40 - $25 = $8w - $5w
$15 = $3w
w = 5
Therefore, Darnell and Lance will have the same amount of money in 5 weeks.
To find out how much money each boy will have at that time, we can substitute w = 5 into the equations:
Darnell's savings = $40 + $5(5) = $65
Lance's savings = $25 + $8(5) = $65
Therefore, when they have the same amount of money, both Darnell and Lance will have $65.
If both boys continue saving at the same rate, we can determine who will have $100 first. We can set up an inequality to represent this:
Darnell's savings < Lance's savings
$40 + $5w < $25 + $8w
Simplifying this inequality, we get:
$40 - $25 < $8w - $5w
$15 < $3w
w > 5
Therefore, if both boys continue saving at this rate, Darnell will have $100 first.