Question

nico was stunned when he opened the mail.Here was a check for $332.50 this is the interest he earned on his investment.One year ago Nico had been given 5,000.His parents made him put it in the bank and save it for college,but the said he could keep the interest it earned each year.A portion of his money is deposited in a high rate account that earned 8% annual interest.The rest is in a regular account that earned 3% this year.Both accounts pay simple interest computed at the end of the year.how much of Nicos money was invested in each account.

Answer 1

@amistre64

Answer 2

@Isaiah.Feynman

Answer 3

@Isaiah.Feynman

Answer 4

@amistre64

Answer 5

@phi

Answer 6

Do you know the formula for "simple interest" ?

Answer 7

I=prt

Answer 8

now we have to figure out how to use it for your problem.

Answer 9

ok

Answer 10

How much time are we talking about? can you figure that out by reading the question ?

Answer 11

year

Answer 12

yes, 1 year. that means t= 1 in your formula (for both rates)
next, we have two rates. what are they ?

Answer 13

8 and 3

Answer 14

I think we have to be more careful. not just 8 and 3. what about the percent ?

Answer 15

Do you understand that 8% is different from just 8? And when we do these problems we have to write the rate as a *decimal* number. Can you write 8% as a decimal?

Answer 16

i kno

Answer 17

Can you write 8% as a decimal?

Answer 18

0.08

Answer 19

ok. Now let's write what we know about the interest for part of the money invested at 8%:
I = P R T

T=1 (1 year)
R = 0.08 (8% per year)
P = ? we don't know (and it's what we have to find to answer the question)
let P = x (x for unknown)

I = x * 0.08 * 1

multiplying by 1 does not do anything, so let's simplify to just

I = 0.08x (this means 0.08 * x)
ok so far ?

Answer 20

yes

Answer 21

If we call the amount invested at 3% "y" , can you try writing the same type of equation for the amount invested at 3% ?

Answer 22

the equation for 3% is 0.03x

Answer 23

ok but it's better to say
Interest= 0.03x just to help remember what it stands for.

Now we use this idea: the sum of both interests add up to what number ?

Answer 24

and we have to be more careful. x is the amount invested at 8%
that amount invested at 3% is probably not the same amount, so we should call it y
(otherwise we will get confused)
so
I= 0.8x
I2 = 0.03y (I2 is to show it's a different interest)

the total interest we get is I+I2 = ? (read the problem)

Answer 25

0.8x+0.03x

Answer 26

almost. do you understand that we should not use 0.03x , it should be 0.03y
?

Answer 27

and somehow 0.08 was wrongly changed to 0.8 oops!

Answer 28

also
a check for $332.50 this is the interest he earned on his investment.

in other words the total of the two interests is that amount.

can you try again?

Answer 29

0.08x+0.03y=332.50

Answer 30

ok, now it looks good.

next, any idea what x+y add up to ? (remember x and y are the amounts we invest)

Answer 31

0.11

Answer 32

don't confuse the interest rates. x and y are the principal (amount of money)
how much money was invested? (read the problem, it tells you)

Answer 33

5,000

Answer 34

do you see x+y= 5000
and we split the 5000 into x for the 8%, and y for the 3% ?

Answer 35

Here is what we know
0.08x+0.03y=332.50
x + y = 5000

do you know how to solve a system of equations ?

Answer 36

no

Answer 37

@phi

Answer 38

we can use substitution.
start with
x+y= 5000
can you "solve for y" ? (add -x to both sides)