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?

- anonymous

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- anonymous

come on guys u can do it please help!

- anonymous

simple interest or compound???

- anonymous

idk what either of that is

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## More answers

- anonymous

u should use the formula I= prt

- anonymous

what is the formula
is it
\[\large{I= Prt}\]
or, \[\large{A= P\times(1+r)^n}\]

- anonymous

i was taught to use I = prt but whatever is easiest

- anonymous

ok that is the formula for simple interest

- anonymous

ok so shami and reese have deposited the amount for the same amount of time right

- anonymous

uh yeah guess

- anonymous

ok let us assume shami has deposited amount x
so reese will deposit how much???

- anonymous

x-200

- anonymous

Sharmi deposits $200 less than Reese.

- anonymous

correct your value

- anonymous

it would be x+200

- anonymous

oh ok

- anonymous

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

- anonymous

so 100= x(0.5) t ???

- anonymous

no r = 5% = 5/100 = 0.05

- anonymous

\[100= x(0.05) t\] ???

- anonymous

yes now solve for t

- anonymous

but the answer choices give two solutions

- anonymous

ok wait first solve for t

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

is it 600 ??

- anonymous

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

- anonymous

ok thank you so much!

- anonymous

have u understood how to solve

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