Santiago receives $143 per year in simple interest from three investments. Part is invested at 2%, part at 3%, and part at 4%. There is $500 more invested at 3% than at 2%. The amount invested at 4% is three times the amount invested at 3%. Find the amount of each rate
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The amount of each rate of interest given the total simple interest received is

$400, $900 and $2,700 respectively

let

a = 2% investment

= 0.02

b = 3% investment

= 0.03

c = 4% investment

= 0.04

Total interest = (0.02×a) + (0.03×b) + (0.04×c)

143 = 0.02a + 0.03b + 0.04c (1)

b = a + 500 (2)

c = 3b (3)

substitute (3) into (1)

143 = 0.02a + 0.03b + 0.04(3b)

143 = 0.02a + 0.03b + 0.12b

0.02a + 0.15b = 143 (4)

from (2)

b - a = 500 (5)

multiply (5) by 0.02

0.02b - 0.02a = 10

0.02a + 0.15b = 143 (4)

Add

0.02b + 0.15b = 10 + 143

0.17b = 153

b = 900

substitute b into (3)

c = 3b (3)

c = 3(900)

c = 2700

Recall,

b = a + 500 (2)

900 = a + 500

900 - 500 = a

a = 400

Therefore, the amount of each rate of interest given the total simple interest received is $400, $900 and $2,700 respectively

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02a+.03b+.04c=126,

b=a+500,

c=3b

a=300., b=800., c=2400.

Step-by-step explanation: