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.

double post. See later answer

To solve this problem, we can set up a system of equations. Let's call the amount of money in Amelia's parents' account P, and the amount of money in her grandparents' account G.

From the given information, we know that the total amount of money in the two accounts at the beginning of the year is $6400, so our first equation is:

P + G = $6400 (equation 1)

We also know that the interest earned by the parents' account is 5% and the interest earned by the grandparents' account is 8%, and the total interest earned by both accounts is $460. We can set up another equation for the interest earned:

0.05P + 0.08G = $460 (equation 2)

Now we can solve this system of equations to find the values of P and G.

First, we can multiply equation 1 by 0.05 to make the coefficients of P in both equations the same:

0.05P + 0.05G = $320 (equation 1 multiplied by 0.05)

Now subtract this equation from equation 2:

(0.05P + 0.08G) - (0.05P + 0.05G) = $460 - $320

0.03G = $140

Divide both sides of the equation by 0.03:

G = $140 / 0.03

G = $4666.67

Now substitute this value of G back into equation 1 to find the value of P:

P + $4666.67 = $6400

P = $6400 - $4666.67

P = $1733.33

Therefore, the current value of Amelia's parents' savings account is $1733.33 and the current value of her grandparents' savings account is $4666.67.