1. After 4 weeks, Andre will have more money in their savings account.
2. They will have the same amount of money after weeks.
1. To find the answer, you must first solve to find out how much money each person has.
Andre: He starts with $100, and adds $5 each week. Since their looking for who has more money after 4 weeks, multiply $5 by 4. 5 x 4 = $20. Then add $100 and $20. Andre has $120 after 4 weeks.
Elena: She starts with $10, and adds $20 each week. Following the same steps from that were taken to find Andre's total. Multiply 20 and 4 to get $80. Then add $10 and $80. Elena has $90 after 4 weeks.
Andre has more money by $30.
2. They will have the same amount of money after 6 weeks. To show this use: $100 + ($5 · x) = $10 + ($20 · x).
-Solve the parentheses on both sides. 5 times x = 5x and 20 times x = 20x. The equation now says "$100 + 5x = $10 + 20x.
-Get the "x" terms on one side and the money amounts on the other. To do so, subtract 5x and 10 from both sides. This cancels out the 5x on the left side of the equation (leaving 15x on the right side) and cancels out the 10 on the right side (leaving 90 on the left side). The equation now says "90 = 15x"
-Finally, get "x" by itself. Divide both sides by 15, to get "6 = x" or "x = 6".
Thus meaning they will have the same amount of money after 6 weeks.
To check this, fill in 6 for x in the equation "$100 + ($5 · x) = $10 + ($20 · x)". Then solve.
Andre: $5 x 6 = $30
$30 + $100 = $130.
Elena: $20 x 6 = $120
$120 + $10 = $130
$130 = $130.
I hope this helps!