nicole1217
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?
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nicole1217
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come on guys u can do it please help!
sheg
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simple interest or compound???
nicole1217
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idk what either of that is
nicole1217
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u should use the formula I= prt
sheg
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what is the formula
is it
\[\large{I= Prt}\]
or, \[\large{A= P\times(1+r)^n}\]
nicole1217
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i was taught to use I = prt but whatever is easiest
sheg
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ok that is the formula for simple interest
sheg
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ok so shami and reese have deposited the amount for the same amount of time right
nicole1217
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uh yeah guess
sheg
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ok let us assume shami has deposited amount x
so reese will deposit how much???
nicole1217
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x-200
sheg
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Sharmi deposits $200 less than Reese.
sheg
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correct your value
sheg
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it would be x+200
nicole1217
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oh ok
sheg
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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
\[\large{I= P\times{r}\times{t}}\]
nicole1217
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so 100= x(0.5) t ???
sheg
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no r = 5% = 5/100 = 0.05
nicole1217
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\[100= x(0.05) t\] ???
sheg
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yes now solve for t
nicole1217
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but the answer choices give two solutions
sheg
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ok wait first solve for t
sheg
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on solving for t you will get
\[\large{t= {{100}\over{0.05x}}}= {{10000}\over{5x}}\]
sheg
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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
\[\large{I= P\times{r}\times{t}}\]
sheg
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you will get
\[\large{t= {{90}\over{0.03(x+200)}}}\]
now equate these two equations
nicole1217
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ohhh okay so i solve for sharmi and then reese and thats the answer
sheg
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you will get
\[\large{{10000}\over{5x}}= \large{{90}\over{0.03(x+200)}}\]
now solve for x
nicole1217
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is it 600 ??
sheg
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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
nicole1217
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ok thank you so much!
sheg
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have u understood how to solve