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A bank loaned out $30,000, part of it at the rate of 15% annual interest, and the rest at 10% annual interest. The total interest earned for both loans was $3,550.00. How much was loaned at each rate?

Answer :

2134jenny

Answer:

x represent the value loaned at 15% and y represent the value loaned at 10%.

[tex]x=11000[/tex] and [tex]y=19000[/tex]

Step-by-step explanation:

We are going to write a system of two linear equations. The first equation  will represent the total amount loaned.

[tex]x+y=30000[/tex]

Now the second equation are will represent the interest earned for both loans.

[tex](x*0.15)+(y*0.10)=3550[/tex]

Then x represent the value loaned at 15% and y represent the value loaned at 10%. Now solving the equation system we have:

[tex]x=30000-y[/tex] using this in the other equation to find y

[tex]((30000-y)0.15)+(0.10*y)=3550[/tex]

[tex]4500-0.15y+0.10y=3550[/tex]

[tex]4500-0.05y=3550[/tex]

[tex]4500-3550=0.05y[/tex]

[tex]950=0.05y[/tex]

[tex]\frac{950}{0.05}=y[/tex]

[tex]19000=y[/tex]

With the value of y we can find x

[tex]x=30000-19000[/tex]

[tex]x=11000[/tex]

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