SOLUTION: Mark invested his money at 9% interest rate while Sarah invested her money at 5% interest rate. If Mark invested $1,000 more than what Sarah did and the combined amount of interest

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Question 1154337: Mark invested his money at 9% interest rate while Sarah invested her money at 5% interest rate. If Mark invested $1,000 more than what Sarah did and the combined amount of interest earned after a year is $790.00, how much did each person invest?
Answer by ramkikk66(644) About Me  (Show Source):
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Ans:
Say Mark invested x dollars.
Then Sarah invested (x - 1000) dollars
Interest earned by Mark = x+%2A+0.09
Interest earned by Sarah = %28x+-+1000%29+%2A+0.05 = 0.05x+-+50
Total interest = 790
So we have the equation
0.09x+%2B+0.05x+-+50+=+790
Moving constants to one side and variables to the other side
0.14x+=+840 or x+=+6000
So Mark invested 6000 dollars and Sarah invested (6000 - 1000) = 5000 dollars.
Check
Interest for Mark = 6000+%2A+0.09+=+540
Interest for Sarah = 5000+%2A+0.05+=+250
Total interest = 540+%2B+250+=+790 Check successful!
Ans: Mark = $6000, Sarah = $5000