Solve the equation algebraially

Question

Lauren deposits a total of $11,500 in savings account at two different banks. The first bank pays 4.5% interest, while the second bank pays 6% interest. If she earns a total of $637.50 in interest in one year, how much was deposited at each bank?

Answer 1

Aryan,

 

Let  "x" be the amount of money placed in the first bank. Since Lauren deposited $11,500 total in both banks, then she deposited "11,500-x" into the second bank. Now, if we multiply the amount deposited into a bank times the interest rate of the bank, that will give us the total interest earned from that bank. If we do this for both banks and add the results, we will obtain the total interest earned for the year. However, we know that the result is 637.50!  So, our equation looks like:

 

.045x+(11,500-x)(.06)=637.50    (4.5%=.045  and 6%=.06)       

 

.045x+690-.06x=637.50

 

-.015x=-52.50

 

x=3,500          So Lauren deposited $3,500 into the first bank!

 

Since we know she invested $11,500 total, she must have deposited $8,000 into the second bank.