Last year, Teresa had $ 30,000 to invest. She invested some of it in an account that paid 5 % simple interest per year, and she invested the rest in an account that paid 9 % simple interest per year. After one year, she received a total of $ 1700 in interest. How much did she invest in each account? Click on "Explain" if you need help.

Question

19-05-2015
Mathematics

Answered

Last year, Teresa had $ 30,000 to invest. She invested some of it in an account that paid 5 % simple interest per year, and she invested the rest in an account that paid 9 % simple interest per year. After one year, she received a total of $ 1700 in interest. How much did she invest in each account? Click on "Explain" if you need help.

Answer :

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lovelybird lovelybird · Answer 1 · 2015-05-19T15:05:14-04:00

I hope it is right

The total amount of investment is $30,000 and it was invested into two account.
Called "a" for the first account and "b" for the second account of the rest money. Therefore

a+b= 30,000 => a = 30,000 - b

The first account has paid with 5% interest and second paid with 9% ( anually), and finally she recieve the total of interest is 1,700. Therefore,
The sum of both interest must equal 1,700

(a x 5% ) + (b x 9%) = 1,700
0.05a + 0,09b = 1,700

a = 30,000 - b. (below)

0,05 x (30,000 - b) + 0,09b = 1,700

1,500 - 0,05b + 0,09b = 1,700
b = 5,000 then use it into ( a= 30,000 -b = 30,000-5,000 = 25,000)

So the first investment is 5,000 and second is 25,000