A city zoo borrowed $2,000,000 at simple annual interest to construct a breeding facility. Some of the money was borrowed at 3%, some at 5%, and some at 10%. Use a system of equations to determine how much was borrowed at 5% if the total annual interest was $105,000 and the amount borrowed at 3% was twice the amount borrowed at 10%. Solve the system using matrices.
A)$700,000 was borrowed at 5%
B)$500,000 was borrowed at 5%
C)$1,600,000 was borrowed at 5%
D)$1,000,000 was borrowed at 5%
E)$100,000 was borrowed at 5%

Question

Quizplus · Accepted Answer

Let x, y, and z represent the amounts borrowed at 3%, 5%, and 10% respectively. The system of equations based on the given information is:1. x + y + z = 2,000,000 (total amount borrowed)2. 0.03x + 0.05y + 0.10z = 105,000 (total interest)3. x = 2z (amount at 3% is twice the amount at 10%)Using matrices to solve, we first express the system in matrix form as AX = B, where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.A = [[1, 1, 1], [0.03, 0.05, 0.10], [2, 0, -1]]X = [[x], [y], [z]]B = [[2,000,000], [105,000], [0]]Solving for X gives the amounts borrowed at each rate. The solution shows that $500,000 was borrowed at 5%.

A City Zoo Borrowed $2,000,000 at Simple Annual Interest to Construct