a woman has money in two accounts one account pays 7 annual

a woman has money in two accounts one account pays 7% annual interest , whereas the others pay 15% annual interest if she has $ 1500 more invested at 15 % than she does at 7% and her total for a yera is $ 1545 how much money does she have in each account? the answer is $6000 for 7% and 7500 at 15 % but i need the work solution for that !

Solution

Suppose she has $ x in the account with 7% interest and $ y in the account with 15% interest.

Interest earned on these accounts for year would be $7x/100 and $15y/100. Thus two equations are formed as follows:

y= x +1500 and 7x/100 + 15y/100 = 1545, or 7x+15y=154500. Now, substituting for y from the first equation, it becomes 7x +15(x+1500)=154500

Or, 7x +15x = 154500- 22500

22x= 132000

x= 132000/22= 6000 and therefore y= 6000+1500= 7500

Answer is therefore, amount invested at 7% interest is $6000 and amount invested at 15% interest is $7500

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