Answer:
Business equipment loan = $12,994
small business loan = $23,027
Home equity loan = $39,979
Explanation:
Let;
x denote the business equipment loan amount
y denote the small business loan amount
z denote the home equity loan amount
Therefore;
x + y + z = $76,000......equation 1
Simple interest on;
loan x = 11% 0f x = 0.11x
loan y = 5% of y = 0.05y
loan z = 4.5% 0f z = 0.045z
Total simple interest due on the loans = $4380
therefore;
0.11x + 0.05y + 0.045z = 4380......equation 2
Annual interest on home equity loan (z) was $370 more than interest on business equipment loan (x),
Therefore;
0.045z = 0.11x + 370......equation 3
z = 0.11x/0.045 + 370/0.045
z = 2.444x + 8222.22......equation 4
<em>if we substitute equation 3 into equation 2, we have;</em>
0.11x + 0.05y + (0.11x + 370) = 4380
0.22x + 0.05y = 4380 -370
0.22x + 0.05y = 4010
0.05y = 4010 - 0.22x
y = 4010/0.05 - 0.22x/0.05
y = 80200 - 4.4x......equation 5
<em>if we substitute equations 4 and 5 into equation 1, we have;</em>
x + y + z = 76000
x + (80200 - 4.4x) + (2.444x + 8222.22) = 76,000
80200 + 8222.22 - 76,000 = 4.4x - 3.444x
12422.22 = 0.956x
x = 12422.22/0.956
x = 12993.96
<em>This means her business equipment loan was $12,994</em>
From equation 5
y = 80200 - 4.4x
y = 80200 - 4.4 (12993.96)
y = 23026.59
<em>This means her small business loan was $23,027</em>
From equation 4
z = 2.444x + 8222.22
z = 2.444 (12993.96) + 8222.22
z = 39,979.4
<em>This means her home equity loan was $39,979</em>
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