Amelia's parents and grand parents have both opened savings accounts to save for Amelia's education this year. Amelia's parents' savings account earned 5% interest and her grandparents account earned 8% interest. This year the two savings accounts have earned a total of $460 in interest. At the beginning of the year, the two accounts were worth a total of $6400. Determine the current values of both savings account.
Designate the beginning value of one account as X and the other as $6400 - X. This leads to the following formula:
.05X + .08(6400 - X) = 460
Solve for X to determine the original amount for the parents and work from there.
I hope this helps. Thanks for asking.
To solve the equation .05X + .08(6400 - X) = 460, you need to distribute the .08 to both terms inside the parentheses:
.05X + .08 * 6400 - .08 * X = 460
This simplifies to:
.05X + 512 - .08X = 460
Combine like terms by subtracting 512 from both sides:
.05X - .08X = 460 - 512
-0.03X = -52
Divide both sides by -0.03 to isolate X:
X = (-52) / (-0.03)
X ≈ 1733.33
Now that you have X, you can find the value of the parents' savings account. The grandparents' savings account would then be 6400 - X.
Parents' savings account value = X ≈ $1733.33
Grandparents' savings account value = 6400 - X ≈ $4666.67
So, the current values of both savings accounts are approximately $1733.33 for the parents and $4666.67 for the grandparents.