Answer:
(1) x + y = 20,000
0.03x + 0.05y = 800
(2) $10,000 was invested in the first account that yielded 3% interest and $10,000 was also invested in the second account that yielded 5% interest.
(3) $5000 should be invested in the first account and $15,000 should be invested in the second account.
Step-by-step explanation:
The total money invested by Hanai is given to be $ 20,000.
Note: she invested in two different account, one yielded 3% interest and the other yielded 5% interest.
We need to know the amount of money invested in each account that brought about the interest.This means that we must find the amount invested in the first part that yielded 3% and the amount in the second part that yielded 5%.
Let x represent the amount in Part A that yielded 3% and y represents the amount in part B that yielded 5%.
From the first statement , we have
x + y = 20000 ................... equation 1
It was also given that The investment returned $800.
Recall that Interest = PTR/100
Since the time is not given , then we will use Interest = PR
This means that we can use this to calculate interest earned on both accounts , that is
Part A
I = 3%
P = x
Therefore interest earned in part A will be given as : 3% of x , which will be
0.03x
Also for part B interest earned will be : 5% of y , which will be 0.05y. Since we know that the total interest is $800 , then the sum of both interest must be $800 , that is
0.03x + 0.05y = 800 .................... equation 2
Combining the two equations we have:
x + y = 20000 ............ equation 1
0.03x + 0.05y = 800 .............. equation 2
Solving the resulting simultaneous equation by substitution method.
From equation 1 , make x the subject of the formula , that is
x = 20000 - y ............. equation 3
substitute x = 20000 - y into equation 2 , we have
0.03(20000 - y ) + 0.05y = 800
Expanding , we have
600 - 0.03y + 0.05y = 800
600 +0.02y = 800
collecting the like terms, we have
0.02y = 800 - 600
0.02y = 200
y = 200/0.02
y = 10,000
substitute y = 10,000 into equation 3 , we have
x = 20,000 - 10,000
x = 10 ,000
Therefore , Hanai invested $10,000 in the first account and $10,000 in the second account.
In order to make more than $800 , then more money should be invested in the second account that yielded 5% interest. $15, 000 could be invested in this account and $5,000 should be invested in the first account that yielded 3% interest.
Check:
5% of 15,000 = 750
3% 0f 5000 = 150
Adding together , we have $900.
