SOLUTION: Last year Miley Cyrus earned a total of $784 in interest from 2 investments. Suppose that she invested a total of $28,000, part of it at 2.4% and the rest at 3.1%.How much did she

Question 799410: Last year Miley Cyrus earned a total of $784 in interest from 2 investments.
Suppose that she invested a total of $28,000, part of it at 2.4% and the rest at 3.1%.How much did she initially invest at each rate.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let a = the amount invested at 2.4%
Let b = the amount invested at 3.1%
The total amount invested is given by
(1) a + b = 28,000
The total interest earned is given by
(2) 0.024*a + 0.031*b = 784
Solve (1) for a and substitute it into (2) to get
(3) 0.024*(28000 - b) + 0.031*b = 784 or
(4) 672 - 0.024*b + 0.031*b = 784 or
(5) 0.007*b = 784 - 672 or
(6) 0.007*b = 112
(7) b = 112/0.007 or
(8) b = 16000
Now use (1) to find a as
(9) a + 16000 = 28000 or
(10) a = 28000 - 16000 or
(11) a = 12000
Always check your answer. Use (2) to do it.
Is ( 0.024*12000 + 0.031*16000 = 784)?
Is (288 + 496 = 784)?
Is (784 = 784)? Yes
Answer: Miley Cyrus initially invested $12,000 @ 2.4% and $16,000 @ 3.1%.

RELATED QUESTIONS
A state employees' pension fund invested a total of one million dollars in two accounts... (answered by CPhill)

Hi I'm having a hard time solving this word problem, I hope you could help me with this... (answered by ikleyn)

Last year, Ivanna had $10,000 to invest. She invested some of it in an account that paid... (answered by josgarithmetic)

Anita invested a certain amount of money into a savings account, and invested twice that... (answered by checkley77)

Anita invested a certain amount of money into a savings account, and invested twice that... (answered by stanbon)

The amount of money a broker invested in bonds was double of what she invested in a... (answered by richwmiller)

Sarah invested a certain amount of money into a savings account, and invested 3 times... (answered by ptaylor)

kate invests money in two plans. She invests three-fifths of the money in an account at a (answered by mananth)