Question

Johnny invested $20,000.A portion returned 5% and another portion returned 8%. The total interest earned on the investment was $1150. Write a system of equations for this situation and determine how much of the original investment was invested at the 5% rate and how much was invested at the 8% rate. Answer: Let x be the amount invested that earned 5% and y be the amount invested that earned 8%. System of equations:

Answer 1

Amount invested that yielded interest of 5% is $15000 and amount invested that yielded interest of 8% is $5000

Explanation:

Johnny invested $20,000

We are told that it consisted of 2 portions because one returned an interest of 5% and the other one 8%

Now, Let x be the amount invested that earned 5% and y be the amount invested that earned 8%

Thus:

x + y = 20000 - - - (eq 1)

The total interest earned on the investment was $1150

Thus;

5%x + 8%y = 1150

This can be rewritten as;

0.05x + 0.08y = 1150 - - -(eq 2)

From eq 1, let's make x the subject.

x = 20000 - y

Putting 20000 - y for x in eq 2 gives;

0.05(20000 - y) + 0.08y = 1150

1000 - 0.05y + 0.08y = 1150

Rearranging, we have;

0.03y = 1150 - 1000

0.03y = 150

y = 150/0.03

y = 5000

Thus,

x = 20000 - 5000

x = 15000

Thus,

Amount invested that yielded 5% is $15000 and amount invested that yielded 8% is $5000