An investment of $34000 was made by a business club, The investment was split in

Question

An investment of $34000 was made by a business club, The investment was split into three parts and lasted for one year. The first part of the investment earned 8% interest, the second 6%, and the third 9%. Total interest from the investments was $2700. The interest from the first investment was 4 times the interest from the second. Find the amounts of the three parts of the investment. What is the amount of the first part of the investment? $____ What is the amount of the second part of the investment? $___ What is the amount of the third part of the investment? $___

Explanation / Answer

Solution:

total amount invested = $34000

we know that the amount was split into three parts, let the parts be x, y, z

then, x + y + z = 34000 //Equation 1

interest of any part after a year = the amount of the part times it's interest

interest of first part after a year = x* 0.08 // 8% = 8 / 100 = 0.08

interest of second part after a year = y * 0.06

interest of third part after a year = z * 0.09

we know that the toal interest earned by the total investment = $2700

i.e, 0.08x + 0.06y + 0.09z = 2700 // Equation 2

given that interest from the first investment was 4 times the interest from the second.

i.e, 0.08x = 4 * 0.06y

= x = 3y // substituting this relation in the above eauations

x + y + z = 34000 //Equation 1

3y + y + z = 34000

= 4y + z = 34000 //Equation 3

0.08x + 0.06y + 0.09z = 2700 // Equation 2

= 0.08(3y) + 0.06y + 0.09z = 2700

=0.3y + 0.09z = 2700 // simplyfying the equation by multiplying with 100

= 30y + 9z = 270000 // Equation 4

Solving 3 and 4 equations;

36y + 9z = 306000 //Equation 3 multiplied by 9 to make it simple to solve with equation 4

30y + 9z = 270000

6y = 36000

y = 36000 / 6 = 6000// second part of the investment

x = 3y = 3 * 6000 = 18000 // first part of the investment

z = 34000 - (x + y) // from equation 1

z = 34000 - 24000 = 10000 // third part of the investment

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