Lin and han's families provide money for their school lunch accounts
Han starts with $100 in his account. He spends $15 each week on lunches.
Lin starts with $25 in her account and does not spend any of it. Her family adds $10 each week to her account.
1.At the end of 4 weeks, who has more money in their account? Explain how you know.
2.After how many weeks will Han and Lin have the same amount of money in their lunch accounts?
1. After 4 weeks, Han will have $100 - ($15 * 4) = $40 left in his account.
Lin will have $25 + ($10 * 4) = $25 + $40 = $65 in her account.
Therefore, Lin has more money in her account after 4 weeks.
2. Let's denote the number of weeks as x. After x weeks, Han will have $100 - ($15 * x) in his account.
Lin will have $25 + ($10 * x) in her account.
To find the number of weeks when they have the same amount of money, we can set up an equation:
100 - 15x = 25 + 10x
Combining like terms, we get:
5x = 75
Dividing both sides by 5, we find that x = 15.
Therefore, after 15 weeks, Han and Lin will have the same amount of money in their lunch accounts.
1. At the end of 4 weeks, let's calculate how much money Han and Lin will have in their accounts:
Han:
Starting money: $100
Amount spent each week: $15
Total amount spent in 4 weeks: $15 x 4 = $<<15*4=60>>60
Money remaining in Han's account: $100 - $60 = $<<100-60=40>>40
Lin:
Starting money: $25
Amount added each week: $10
Total amount added in 4 weeks: $10 x 4 = $<<10*4=40>>40
Money remaining in Lin's account: $25 + $40 = $<<25+40=65>>65
Therefore, at the end of 4 weeks, Lin has more money in her account ($65) compared to Han ($40).
2. To determine after how many weeks Han and Lin will have the same amount of money in their lunch accounts, we can set up an equation to find the week number at which their account balances are equal.
Let's denote the number of weeks as "w."
Han's account balance after w weeks: $100 - $15w
Lin's account balance after w weeks: $25 + $10w
To find when their balances are equal, we can set up the equation:
$100 - $15w = $25 + $10w
Simplifying the equation, we get:
$100 - $25 = $10w + $15w
$75 = $25w
w = $75/$25
w = 3
Therefore, after 3 weeks, Han and Lin will have the same amount of money in their lunch accounts.