Question

HELPP!!! I need someone to walk me through this problem!!
A company placed $1,000,000 in three different accounts. It placed part in short-term notes paying 4.5% per year, twice as much in government bonds paying 5%, and the rest in utility bonds paying 4%. The income after one
year was $45,500. How much did the company place in each account?

Answer 1

@jim_thompson5910

Answer 2

@xapproachesinfinity @TheSmartOne

Answer 3

Let

x = amount (in dollars) invested in short term notes
y = amount (in dollars) invested in government bonds
z = amount (in dollars) invested in utility bonds

Answer 4

"A company placed $1,000,000 in three different accounts"

so that means we have this equation

x+y+z = 1000000

Answer 5

we know that "twice as much in government bonds " were invested compared to short term notes, which means we have y = 2x

Answer 6

so we can go back to the first equation x+y+z = 1000000 and plug in y = 2x

x+y+z = 1000000

x+2x+z = 1000000

3x+z = 1000000

Answer 7

I thought it would be
x= 1000000
y= 1000000
z= 1000000
Because the company placed it in three different accounts

Answer 8

no I think that 1 million dollar figure is the total spread out the 3 accounts

Answer 9

ok

Answer 10

If it was like that, then the answer to "How much did the company place in each account?" is simply "1 million dollars each"

Answer 11

oh ok

Answer 12

anyways, "It placed part in short-term notes paying 4.5% per year"

so it earns 0.045x dollars from short-term notes

------------------------

"government bonds paying 5%" ---> earns 0.05y dollars from government bonds

-------------------------

"utility bonds paying 4%" ---> earns 0.04z dollars with utility bonds

Answer 13

in total, it earns 0.045x + 0.05y + 0.04z dollars

Answer 14

"The income after one year was $45,500", so we can say

0.045x + 0.05y + 0.04z = 45500

Answer 15

Now plug in y = 2x

0.045x + 0.05y + 0.04z = 45500

0.045x + 0.05(2x) + 0.04z = 45500

0.045x + 0.10x + 0.04z = 45500

0.145x + 0.04z = 45500

Answer 16

after all this, we get this system of equations

3x+z = 1000000
0.145x + 0.04z = 45500

Answer 17

wait where did 3x come from?

Answer 18

I plugged y = 2x into x+y+z = 1000000, then combined like terms

Answer 19

OHH alright

Answer 20

i can solve it from here thnx!

Answer 21

tell me what you get so I can check

Answer 22

ok

Answer 23

-0.04*(3x+z = 1000000)
0.145x + 0.04z = 45500
--------------------
-0.12x -0.04 = -40000
0.145x +0.04 = 45500

Answer 24

-0.12x -0.04z = -40000
0.145x +0.04z = 45500

Answer 25

0.025x = 5500
x = 220000

Answer 26

very good

Answer 27

so y = ??

Answer 28

hold up i got this

Answer 29

I found z first, though, before getting the y because it was faster.
3x+z = 1000000
3(220000) + z = 1000000
660000 + z = 1000000
z = 340000

Answer 30

good, and I'm sure you see how to get y from x

Answer 31

x+y+z = 1000000
220000 + y + 340000 = 1000000
560000 + y = 1000000
y = 440000

Answer 32

or you can say y = 2x ---> y = 2*(220,000) = 440,000

either way works

Answer 33

oh yeah that was probably easier :)

Answer 34

because we let

x = amount (in dollars) invested in short term notes
y = amount (in dollars) invested in government bonds
z = amount (in dollars) invested in utility bonds

and because you found that

x = 220,000
y = 440,000
z = 340,000

this means

$220,000 was invested in short term notes
$440,000 was invested in government bonds
$340,000 was invested in utility bonds

Answer 35

you got all 3 correct

Answer 36

yayy!

Answer 37

thnx for all the help! i gave u a medal :)

Answer 38

thx and I'm glad it's clicking now