Answer:
a 54,000 dolllars
b 18,000 dollars
c 10,000 dollars
Explanation:
From the given we can conclude:
all investment equal 82,000 thus:
82,000= a + b + c
then:
interest of a equal 4 times interest of b:
a x 0.08 = 4 x b x 0.06
a = (0.24/0.08)b = 3b
and that total interest:
a x 0.08 + b x 0.06 + c x 0.09 = 6,300
4 x b x 0.06 + b x 0.06 + c x 0.09 = 6,300
5bx0.06 + 0.09c = 6,300
c = (6,300 - 0.3b)/0.09
we now replace a and c as expressions of b:
82,000 = 3b + b + c = 4b + c
82,000 = 4b + (6,300 - 0.3b)/0.09
82,000 = 4b + 70,000 - 3,33b
12,000 = (2/3)b
b = 18,000
now we solve for a and c:
a = 3b = 3 x 18,000 = 54,000
interest of b:
18,000 x 0.06 = 1,080
interest of a:
54,000 x 0.08 = 4.320
4,320/1,080 = 4 we pass the interest relathionship requirement
82,000 - 54,000 - 18,000 = c
c= 10,000
10,000 x 0.09 = 900
1,080 + 4,320 + 900 = 6,300 we also fullfil the total interst requirement
