A student takes out a loan at a 3% interest and then must pay 5% for any additional money. If the student borrows 10,000 more at 5% than at 3%, then the total interest for 1 year is $1,200. How...

A student takes out a loan at a 3% interest and then must pay 5% for any additional money. If the student borrows 10,000 more at 5% than at 3%, then the total interest for 1 year is $1,200. How much does the student borrow at each rate? please show the work

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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Let us say that the student has borrowed $X amount at 3% interest. 

It is given that he has borrowed 10000 at 5% than at 3%. So he should have a load for $(X+10000) amount at 5%.

Interest for 3% rate loan (R1) = 3/100*X

Interest for 5% rate loan` (R2) = 5/100*(X+10000)`

 

It is given that total interest per one year is $1200.

So we can say;

`R1+R2 = 1200`

`3/100*X+5/100*(X+10000) = 1200`

`3X+5X+50000 = 1200*100`

`8X = 120000-50000`

`X = 8750`

 

So at 3% interest rate student have taken $8750.

At 5% interest rate he has taken (8750+10000) = $18750

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