Answer:
The principle amounts borrowed by Jason are [tex]$\$ 6000$[/tex] and [tex]$\$ 12000$[/tex] .
Step-by-step explanation:
Given
Jason borrowed [tex]\$18,000[/tex] in two loans.
Step 1 of 2
Let [tex]$x$[/tex], and [tex]$(\$ 18,000-x)$[/tex] be the principle amount borrowed by Jason.
Let [tex]$P_{1}=x$[/tex], and
[tex]$P_{2}=(\$ 18000-x)$[/tex].
Let [tex]$I_{1}$[/tex]be the simple interest paid on loan 1 , and [tex]$I_{2}$[/tex] be the simple interest paid on loan 2 .
[tex]I_{1}+I_{2}=\$ 1380[/tex]
[tex]r_{1}=11 \%[/tex] (interest rate of loan 1)
[tex]$r_{2}=6 \%$[/tex] (interest rate of loan 2)
Time in years for both the loan is 1 year.
Substitute the formula of simple interest.
[tex]$P_{1} r_{1} t+P_{2} r_{2} t=\$ 1380$[/tex]
Step 2 of 2
Substitute the values
[tex](x)(0.11)(1)+(\$ 18,000-x)(0.06)(1)=\$ 1380 \\[/tex]
[tex]&0.11 x+\$ 1080-0.06 x=\$ 1380[/tex]
[tex]&0.05 x+\$ 1080=\$ 1380[/tex]
[tex]&0.05 x=\$ 1380-\$ 1080 \\[/tex]
[tex]&0.05 x=\$ 300 \\[/tex]
[tex]&x=\$ 6000[/tex]
Substitute the value [tex]$\$ 6000$[/tex] in [tex]$(\$ 18,000-x)$[/tex] to find the other principle amount.
[tex]\$ 18,000-\$ 6000=12,000[/tex]
The principle amounts borrowed by Jason are [tex]$\$ 6000$[/tex] and [tex]$\$ 12000$[/tex].
Learn more about simple interest, refer :
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