Answer:
The set of equations are -
a + b = 19,250
(3a/100) + (4b/100) = 750
The initial deposit in the savings account = $2,000
The initial amount in the certificate of deposit = $17,250
Step-by-step explanation:
Now, let us call the savings account that Agatha made the first deposit "a" and call the certificate of deposit she made the second deposit, "b".
We learnt that her total money after one year grew to $20,000 and $750 out of this amount was the total interest she earned over the period. This means that the principals she deposited into the two accounts will be obtained by subtracting the interest from the current value of her money. That is:
$20,000 - $750 = $19,250. So, the sums she deposited into the two accounts totalled $19,250. We have an equation here;
a + b = $19,250 ----- call this equation 1.
Again, we learnt that the first deposit (savings account) paid an interest rate of 3% yearly and the certificate of deposit paid an interest of 4% yearly.
This means that the interest yielded by the deposit in the savings account = 3/100 × a = 3a/100
And the interest yielded by the deposit in the certificate of deposit = 4/100 × b = 4b/100
We know that the interests from these two accounts was equal to $750. We have another equation now:-
3a/100 + 4b/100 = $750 ----- call this equation 2
So we now have 2 equations that can always be used to determine the sums that were deposited in the two accounts.
a + b = 750
3a/100 + 4b/100 = 750
From equation 1 :
a + b = 19,250
a = 19,250 - b
To find the initial deposit into the savings account, we can substitute "a" for 19250 - b in equation 2.
3 × [(1950-b)/100] + (4b/100) = 750
[(5750 - 3b)/100] + (4b/100) = 750
(57750 + b)/100 = 750
57750 + b = 75000
b = 75000 - 57,750
b = 17, 250
We can then substitute "b" for 17,250 in equation 1:
a + 17,250 = 19,250
a = 19,250 - 17,250
a = $2,000
Therefore, the initial deposit in the savings account = $2,000 while the initial deposit made into the certificate of deposit = $17,250
