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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?

Mathematics
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come on guys u can do it please help!
simple interest or compound???
idk what either of that is

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Other answers:

u should use the formula I= prt
what is the formula is it \[\large{I= Prt}\] or, \[\large{A= P\times(1+r)^n}\]
i was taught to use I = prt but whatever is easiest
ok that is the formula for simple interest
ok so shami and reese have deposited the amount for the same amount of time right
uh yeah guess
ok let us assume shami has deposited amount x so reese will deposit how much???
x-200
Sharmi deposits $200 less than Reese.
correct your value
it would be x+200
oh ok
Now in Shami's Case P = $ x r = 5% I = $ 100 Now plug in these values in this equation and solve for t \[\large{I= P\times{r}\times{t}}\]
so 100= x(0.5) t ???
no r = 5% = 5/100 = 0.05
\[100= x(0.05) t\] ???
yes now solve for t
but the answer choices give two solutions
ok wait first solve for t
on solving for t you will get \[\large{t= {{100}\over{0.05x}}}= {{10000}\over{5x}}\]
Similarly in reese's Case P = $ (x+200) r = 3% I = $ 90 Now plug in these values in this equation and solve for t \[\large{I= P\times{r}\times{t}}\]
you will get \[\large{t= {{90}\over{0.03(x+200)}}}\] now equate these two equations
ohhh okay so i solve for sharmi and then reese and thats the answer
you will get \[\large{{10000}\over{5x}}= \large{{90}\over{0.03(x+200)}}\] now solve for x
is it 600 ??
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
ok thank you so much!
have u understood how to solve

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