Hanai invested $20,000, part at 3% interest and part at 5% interest. the
investment returned $800.
what is the system of equations that represents this situation?
how was the original $20,000 investment split between the two interest
rates?
how would the investment need to be split to make more than $800?
how do you know?

(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.