A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility. some of the money was borrowed at 6%, some at 7%, and some at 10%. use a system of linear equations to determine how much was borrowed at each rate given that the total annual interest was $145,500 and the amount borrowed at 6% was twice the amount borrowed at 10%. solve the system of linear equations using matrices.

Question

Kayleigh Oconnor

Business

13 May, 11:26

A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility. some of the money was borrowed at 6%, some at 7%, and some at 10%. use a system of linear equations to determine how much was borrowed at each rate given that the total annual interest was $145,500 and the amount borrowed at 6% was twice the amount borrowed at 10%. solve the system of linear equations using matrices.

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Martin · Answer 1

given:

amount borrowed = $2,000,000.

rate of interests are 6%,7% and 10 % respectively

0.06x+0.10 (1/2x) + 0.07 (2,000,000 - (x+0.5x) = 145,500

:

(0.06+0.05) x+0.07 (2,000,000 - 1.5x) = 145,500

0.11x+140000-0.105x = 145,500

0.005x = 5,500

x = 1,100,000 is the amount borrowed at 6%

1/2*1100,000 = 550,000 is the amount borrowed at 10%

2,000,000-1,650,000 = 350,000 is the amount borrowed at 8%