## nicole1217 4 years ago 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? • This Question is Closed 1. nicole1217 come on guys u can do it please help! 2. sheg simple interest or compound??? 3. nicole1217 idk what either of that is 4. nicole1217 u should use the formula I= prt 5. sheg what is the formula is it $\large{I= Prt}$ or, $\large{A= P\times(1+r)^n}$ 6. nicole1217 i was taught to use I = prt but whatever is easiest 7. sheg ok that is the formula for simple interest 8. sheg ok so shami and reese have deposited the amount for the same amount of time right 9. nicole1217 uh yeah guess 10. sheg ok let us assume shami has deposited amount x so reese will deposit how much??? 11. nicole1217 x-200 12. sheg Sharmi deposits$200 less than Reese.

13. sheg

14. sheg

it would be x+200

15. nicole1217

oh ok

16. sheg

Now in Shami's Case P = $x r = 5% I =$ 100 Now plug in these values in this equation and solve for t $\large{I= P\times{r}\times{t}}$

17. nicole1217

so 100= x(0.5) t ???

18. sheg

no r = 5% = 5/100 = 0.05

19. nicole1217

$100= x(0.05) t$ ???

20. sheg

yes now solve for t

21. nicole1217

but the answer choices give two solutions

22. sheg

ok wait first solve for t

23. sheg

on solving for t you will get $\large{t= {{100}\over{0.05x}}}= {{10000}\over{5x}}$

24. sheg

Similarly in reese's Case P = $(x+200) r = 3% I =$ 90 Now plug in these values in this equation and solve for t $\large{I= P\times{r}\times{t}}$

25. sheg

you will get $\large{t= {{90}\over{0.03(x+200)}}}$ now equate these two equations

26. nicole1217

ohhh okay so i solve for sharmi and then reese and thats the answer

27. sheg

you will get $\large{{10000}\over{5x}}= \large{{90}\over{0.03(x+200)}}$ now solve for x

28. nicole1217

is it 600 ??

29. sheg

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

30. nicole1217

ok thank you so much!

31. sheg

have u understood how to solve