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.