SOLUTION: Question : Nico invests some money at 9% and $1,400 less than that amount of 8%. The investments produced a total of $296 interest in 1 year. How much did he invest at each rate?

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Question 945688: Question : Nico invests some money at 9% and $1,400 less than that amount of 8%. The investments produced a total of $296 interest in 1 year. How much did he invest at each rate?
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How I tried to solve:
Step 1) .09x+.08(x-1,400)=1,400
Step 2) 100( .09x +.08 (x-1,400) = 1,400 (100)
Step 3) 9x+8x-11,200=1,400,000
Step 4) 17x= 1,388,800
Step 5) x= 81,694
Step 6) x-1,400= 81,694
Step 7) x- 1,400 = 81,694- 1,400
Step 8) x= 80,294
Step 9) he invested $81,694 at 9% and $80,294 at 8%
*Step 9 is the two incorrect answers that I got towards this problem. Please help me with a step by step solution to this problem. Thank you.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The investments produced a total of $296 interest in 1 year:
Step 1) .09x%2B.08%28x-1400%29=296
Step 2) 100%28.09x%2B.08%28x-1400%29%29=+296%28100%29
Step 3) 9x%2B8x-11200=29600
Step 4) 17x=+29600%2B11200=40800
Step 5) x=+40800%2F17=>highlight%28x=2400%29
Step 6) x-1400=+2400-1400
Step 7) highlight%28x-+1400+=+1000%29
Step 8) he invested $2400 at 9% and $1000 at 8%
Step 9)+total_investment=2400%2B1000=3400
check:
9% of 2400 is 2400%2A%289%2F100%29=24%2A9=216
8% of 1000 is 1000%288%2F100%29=10%2A8=80
216%2B80=296 which confirms our answer