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?

Question

anonymous · Answer

come on guys u can do it please help!

anonymous · Answer

simple interest or compound???

anonymous · Answer

idk what either of that is

anonymous · Answer

u should use the formula I= prt

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

ok that is the formula for simple interest

anonymous · Answer

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

anonymous · Answer

uh yeah  guess

anonymous · Answer

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

anonymous · Answer

x-200

anonymous · Answer

Sharmi deposits $200 less than Reese.

anonymous · Answer

correct your value

anonymous · Answer

it would be x+200

anonymous · Answer

oh ok

anonymous · Answer

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 · Answer

so 100= x(0.5) t ???

anonymous · Answer

no r = 5% = 5/100 = 0.05

anonymous · Answer

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

anonymous · Answer

yes now solve for t

anonymous · Answer

but the answer choices give two solutions

anonymous · Answer

ok wait first solve for t

anonymous · Answer

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

anonymous · Answer

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 · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

is it 600 ??

anonymous · Answer

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 · Answer

ok thank you so much!

anonymous · Answer

have u understood how to solve