A man invests 5,200, part at 4 and the balance at 3. if his total income gor the two investments is 194 how much money did he invest at each rate?
This has completely gone over my head and I don't understand anything about it. I've tried Khan Academy but still don't understand. Can someone please explain it?

A man invests $5,200, part at 4% and the balance at 3%. If his total income for the two investments is $194, how much money did he invest at each rate?

Let x = amount ($) invested at 4%

then

5200-x = amount ($) invested at 3%

.04x + .03(5200-x) = 194

.04x + 156-.03x = 194

.01x + 156 = 194

.01x = 38

x = $3800 (amount invested at 4%)

amount invested at 3%:

5200-3800 = $1400

Or

Let $x be the amount of money that a man invested in 3% account and $y be the amount of money a man invested at 4% account. The problem can be modelled by the system of two equations.

1. The income for the 1st investment is $0.03x and the income for the 2nd investment is $0.04y.

If his total income for the two investments is $194, then

0.03x+0.04y=194.

2. If a man invests $5,200, part at 4% and the balance at 3%, then

x+y=5,200.

3. You get a system of equations:

x+y=5,200

0.03x+0.04y=194

From the 1st equation express x and substitute it into the 2nd equation:

0.03(5,200-y)+0.04y=194,

156-0.03y+0.04y=194,

0.01y=38

y=3,800

Then x=5,200-3,800=1400

Answer: $1,400 at 3% and $3,800 at 4%.