Andre and elena are each saving money. Andre starts with $100 in his savings account and adds $5 per week. Elena start with $10 in her savings account and adds $20 each week
1.After four weeks, who has more money in their savings account? Explain how you know.
2.After how many weeks will Andre and Elena have the same amount of money in their savings accounts?
1. After four weeks, Andre will have $100 + ($5 * 4) = $100 + $20 = $120 in his savings account.
Elena will have $10 + ($20 * 4) = $10 + $80 = $90 in her savings account.
Therefore, after four weeks, Andre will have more money in his savings account than Elena.
2. We can set up an equation to find out when Andre and Elena will have the same amount of money in their savings accounts:
$100 + ($5 * w) = $10 + ($20 * w)
Where w represents the number of weeks.
Simplifying the equation:
$100 + $5w = $10 + $20w
Rearranging the terms:
$100 - $10 = $20w - $5w
$90 = $15w
Dividing both sides by $15:
w = 6
Therefore, after 6 weeks, Andre and Elena will have the same amount of money in their savings accounts.
1. After four weeks, we can compare the amount of money in Andre and Elena's savings accounts.
Andre's savings:
Initial amount = $100
Amount added per week = $5
Total amount after four weeks = $100 + ($5 * 4) = $100 + $20 = $120
Elena's savings:
Initial amount = $10
Amount added per week = $20
Total amount after four weeks = $10 + ($20 * 4) = $10 + $80 = $90
Therefore, after four weeks, Andre has more money in his savings account with $120 compared to Elena's $90. We reach this conclusion by calculating the total amount each person has after four weeks.
2. To find out how many weeks it will take for Andre and Elena to have the same amount of money in their savings accounts, we can set up an equation:
Andre's savings = Elena's savings
$100 + ($5 * x) = $10 + ($20 * x)
Simplifying the equation, we get:
$100 + $5x = $10 + $20x
Rearranging the equation and combining like terms, we have:
$15x = $90
Dividing both sides by $15, we get:
x = 6
Therefore, Andre and Elena will have the same amount of money in their savings accounts after 6 weeks.