SOLUTION: A man invests $1200, part at 5% and part at 4% per annum, and his total income is $55.50. How much did he invest at each rate?

Algebra.Com
Question 726434: A man invests $1200, part at 5% and part at 4% per annum, and his total income is $55.50. How much did he invest at each rate?
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Part I 5.00% per annum ------------- Amount invested =x
Part II 4.00% per annum ------------ Amount invested = y
1200
Interest----- 55.50

Part I 5.00% per annum ---x *
Part II 4.00% per annum ---y
Total investment
x + 1 y= 1200 -------------1
Interest on both investments
5.00% x + 4.00% y= 55.5
Multiply by 100
5 x + 4 y= 5550.00 --------2
Multiply (1) by -5
we get
-5 x -5 y= -6000.00
Add this to (2)
0 x -1 y= -450
divide by -1
y = 450 - x)
Part I 5.00% $ 750
Part II 4.00% $ 450

CHECK
750 --------- 5.00% ------- 37.50
450 ------------- 4.00% ------- 18.00
Total -------------------- 55.50

RELATED QUESTIONS

Solve this problem by using a two order system. A man invests $5,200, part at 4% and... (answered by nerdybill)
A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two... (answered by ReadingBoosters)
A man has $5000 to invest. He invests part of it at 4 per cent, and the rest at 3 per... (answered by richwmiller)
Joe invests $6000, part at 5% interest and the rest at 7%. If his annual interest income... (answered by mananth)
A man invested $1000, part at 5% and the rest at 6%. His total annual income was $53. (answered by checkley77)
A man invested $2500, part at 4%. His total annual income was $110. How much did he... (answered by checkley77)
A man invested in $4000, part at 5% and the remainder at 3% simple interest. The total... (answered by macston)
Mr.Thompson invests a principal of $8000; part at 8% per annum and the rest at 10% per... (answered by checkley71)
A man invests part of $6,000 at 4% interest and the rest at 3% interest. His total annual (answered by checkley77)