Answer:
Karen has a total amount of $ 101
Maria has a total amount of $ 86
Explanation:
We'll begin by obtaining an expression for the total amount of money in Karen's account. This can be obtained as follow:
Let the number of weeks be x
Let the total amount be y
Karen deposited $ 28 when she opened the account and then deposit $ 5 weekly.
The total amount in x week can be written as:
y = 28 + 5x
For Maria, the total amount in x week is given by:
y = 8x + 7
Next, we shall determine the number of weeks in which they both have the same amount in their account.
For Karen's account, the total amount is:
y = 28 + 5x
For Maria's account, the total amount is:
y = 8x + 7
Total in Karen's = Total in Maraia's
28 + 5x = 8x + 7
Collect like terms
28 – 7 = 8x – 5x
21 = 3x
Divide both side by 3
x = 21/3
x = 7
Thus, they both have the same amount in the 7th week.
Next, we shall determine the total amount in each account in the 7th week. This is illustrated below:
For Karen's account,
y = 28 + 5x
x = 7
y = 28 + 5(7)
y = 28 + 35
y = $ 63
For Maria's account,
y = 8x + 7
x = 7
y = 8(7) + 7
y = 56 + 7
y = $ 63
Finally, we shall determine the total amount in each account 2 weeks after they have the same amount in their account. This is illustrated below:
For Karen's account,
y = 28 + 5x
x = 2
y = 28 + 5(2)
y = 28 + 10
y = $ 38
Total amount = 63 + 38 = $ 101
For Maria's account,
y = 8x + 7
x = 2
y = 8(2) + 7
y = 16 + 7
y = $ 23
Total amount = 63 + 23 = $ 86
SUMMARY:
Karen has a total amount of $ 101
Maria has a total amount of $ 86
