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nicole1217 Group Title

Sharmi and Reese each deposit money into a savings account. Sharmi deposits $200 less than Reese. After the same amount of time, Reese has earned $90 in interest at a rate of 3% per year, and Sharmi has earned $100 in interest at a rate of 5% per year. How much money did Reese and Sharmi initially deposit into their savings accounts?

  • 2 years ago
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  1. nicole1217 Group Title
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    come on guys u can do it please help!

    • 2 years ago
  2. sheg Group Title
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    simple interest or compound???

    • 2 years ago
  3. nicole1217 Group Title
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    idk what either of that is

    • 2 years ago
  4. nicole1217 Group Title
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    u should use the formula I= prt

    • 2 years ago
  5. sheg Group Title
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    what is the formula is it \[\large{I= Prt}\] or, \[\large{A= P\times(1+r)^n}\]

    • 2 years ago
  6. nicole1217 Group Title
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    i was taught to use I = prt but whatever is easiest

    • 2 years ago
  7. sheg Group Title
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    ok that is the formula for simple interest

    • 2 years ago
  8. sheg Group Title
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    ok so shami and reese have deposited the amount for the same amount of time right

    • 2 years ago
  9. nicole1217 Group Title
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    uh yeah guess

    • 2 years ago
  10. sheg Group Title
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    ok let us assume shami has deposited amount x so reese will deposit how much???

    • 2 years ago
  11. nicole1217 Group Title
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    x-200

    • 2 years ago
  12. sheg Group Title
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    Sharmi deposits $200 less than Reese.

    • 2 years ago
  13. sheg Group Title
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    correct your value

    • 2 years ago
  14. sheg Group Title
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    it would be x+200

    • 2 years ago
  15. nicole1217 Group Title
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    oh ok

    • 2 years ago
  16. sheg Group Title
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    Now in Shami's Case P = $ x r = 5% I = $ 100 Now plug in these values in this equation and solve for t \[\large{I= P\times{r}\times{t}}\]

    • 2 years ago
  17. nicole1217 Group Title
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    so 100= x(0.5) t ???

    • 2 years ago
  18. sheg Group Title
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    no r = 5% = 5/100 = 0.05

    • 2 years ago
  19. nicole1217 Group Title
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    \[100= x(0.05) t\] ???

    • 2 years ago
  20. sheg Group Title
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    yes now solve for t

    • 2 years ago
  21. nicole1217 Group Title
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    but the answer choices give two solutions

    • 2 years ago
  22. sheg Group Title
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    ok wait first solve for t

    • 2 years ago
  23. sheg Group Title
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    on solving for t you will get \[\large{t= {{100}\over{0.05x}}}= {{10000}\over{5x}}\]

    • 2 years ago
  24. sheg Group Title
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    Similarly in reese's Case P = $ (x+200) r = 3% I = $ 90 Now plug in these values in this equation and solve for t \[\large{I= P\times{r}\times{t}}\]

    • 2 years ago
  25. sheg Group Title
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    you will get \[\large{t= {{90}\over{0.03(x+200)}}}\] now equate these two equations

    • 2 years ago
  26. nicole1217 Group Title
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    ohhh okay so i solve for sharmi and then reese and thats the answer

    • 2 years ago
  27. sheg Group Title
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    you will get \[\large{{10000}\over{5x}}= \large{{90}\over{0.03(x+200)}}\] now solve for x

    • 2 years ago
  28. nicole1217 Group Title
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    is it 600 ??

    • 2 years ago
  29. sheg Group Title
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    cross multiply you will get 10000*0.03(x+200) = 5x*90 300(x+200) = 450x 300x + 60000 = 450x 450x -300x = 60000 150x = 60000 x = 60000/150 x = 400 so shami deposited $ 400 and reese deposited $400 + $200 = $600

    • 2 years ago
  30. nicole1217 Group Title
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    ok thank you so much!

    • 2 years ago
  31. sheg Group Title
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    have u understood how to solve

    • 2 years ago
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