Question

Last year, Scott had
$20,000
to invest. He invested some of it in an account that paid
6%
simple interest per year, and he invested the rest in an account that paid
10%
simple interest per year. After one year, he received a total of
$1760
in interest. How much did he invest in each account?

Answer 1

@jim_thompson5910

Answer 2

how far did you get with this?

Answer 3

were you able to get started at all?

Answer 4

no .-.

Answer 5

ok let's say we have 2 unknown variables x and y

x = amount of money invested at 6%
y = amount of money invested at 10%

let me know when you're ready for the next step

Answer 6

ok ready

Answer 7

we can only invest money at 6% or 10%. There are no other choices. If we have $20,000 to invest, then that means x and y must add to 20,000

ie

x+y = 20,000

do you agree?

Answer 8

yes

Answer 9

now let's isolate a variable. Let's say we isolate y

how would we get y all by itself? what must we do to both sides?

Answer 10

subtract x ?

Answer 11

yep subtract x from both sides

Answer 12

x+y = 20,000

x+y-x = 20,000-x

y = 20,000 - x

Answer 13

yes

Answer 14

this will be used later. So we'll come back to it

Answer 15

Scott invested x dollars at 6%

How much money does he earn just from this account? Any idea?

Answer 16

does it have to equAL 20000 ?

Answer 17

ignore that part for now

Answer 18

if you had $100 for example, and you earn 6% interest, how much money have you earned?

Answer 19

ummm.

Answer 20

interest = principal*rate*time

principal = amount you invest
rate = interest rate in decimal form
time = time in years (in this case, we'll make the time = 1 to be 1 year)

Answer 21

100 * 6%*1

Answer 22

6% = 6/100 = 0.06

Answer 23

so you'd have 100*0.06*1 = ????

Answer 24

6

Answer 25

yes, so now instead of $100 we don't know what we invest at 6%

so we'd have x*0.06*1 = ????

Answer 26

.06x

Answer 27

that means Scott earned 0.06x dollars so far (from the 6% investment)

x is some unknown number

Answer 28

ok

Answer 29

yes, now Scott also invested y dollars (y is some unknown number) at 10%

how much has Scott earned from just the 10% investment?

Answer 30

x*.10*1

Answer 31

which simplifies to what?

Answer 32

btw use y instead of x

Answer 33

.10y

Answer 34

0.10y

yes

Answer 35

Scott earned 0.06x dollars from the 6% account
he also earned 0.10y dollars from the 10% account

in total, he earned 0.06x+0.10y dollars

do you agree?

Answer 36

yes

Answer 37

we're also told that `After one year, he received a total of $1760`

so that must mean the expression I just got is equal to 1760, so,

0.06x+0.10y = 1760

make sense?

Answer 38

yes

Answer 39

we now go back to `y = 20,000 - x`

replace every copy of 'y' in the the second equation with 20,000-x

so we'd go from
0.06x+0.10y = 1760
to
0.06x+0.10(20,000 - x) = 1760

Don't forget about the parenthesis. From here, you would solve for x

Answer 40

19999.719

Answer 41

i need the amount separately. hm he invested in one account and then the other,

Answer 42

how did you get 19999.719 ?

Answer 43

mathway cx

Answer 44

it's better to do it by hand on pencil and paper

Answer 45

what would be the first step to solve `0.06x+0.10(20,000 - x) = 1760` ?

Answer 46

ok idk how to do this.. i have so many more problemsss .-.

Answer 47

distribute the 0.10 through. What do you get?