Systems of Linear Equations in Applications: "Devon invested $8000 in 3 funds...."

[NoGoodAtMath]

Systems of Linear Equations in Applications: "Devon invested $8000 in 3 funds...."

Devon invested $8000 in three different mutual funds. A fund containing large cap stocks made 6.2% return in 1 year. A real estate fund lost 13.5% in 1 year, and a bond fund made 4.4% in 1 year. The amount invested in the large cap stock was twice the amount invested in the real estate fund. If Devon had a net return of $66 across all investments, how much did he invest in each fund?

Now, I'm using the last application I posted here as a model for this application. Here goes...

[A] = Large cap fund
= Real estate fund
[C]=Bond fund

a+b+c= 8,000
a+b=16,000
62a-135b+44c=66,000

I'm not certain the 16,000 should be there, however, the application did say the amount invested in the large cap fund was TWICE the amount invested in the real estate fund. So, how have I done so far?

 

[skaa]

The amount invested in the large cap stock was twice the amount invested in the real estate fund. It means:
a=2b
And:
62a-135b+44c=66
Everything else is correct.

 

[NoGoodAtMath]

******* should simply be: a = 2b
Which means 2b+b+c = 8000 : 3b + c = 8000

Hokay?

No, I don't understand.

 

[Steven G]

No, I don't understand.

If a+b = 16,000 then how could a+b+c only be 8,000???

Let's take this slowly. The amount invested in the large cap stock was twice the amount invested in the real estate fund


The amount invested in the large cap stock is A

was is just the past tense of is which means =

twice means two times

the amount invested in the real estate fund is B

So, The amount invested in the large cap stock was twice the amount invested in the real estate fund is the same as A = two times B or A = 2B

Now if A = 2B and you said that a+b+c = 8,000 then instead of a we can put 2b. S0 2b + b+c=8000. But 2b +b=3b, so 3b+c=8,000

 

[stapel]

a+b+c= 8,000
a+b=16,000 *******
62a-135b+44c=66,000

******* should simply be: a = 2b
Which means 2b+b+c = 8000 : 3b + c = 8000

Hokay?

No, I don't understand.

If a + b + c equals 8,000, then the only way a + b could equal more than this would be for a or b to be negative. This makes no sense. Also, the second bit of information provided was not that the sum of the amounts invested in A and B was twice what was invested in A, B, and C; but that the amount invest in A was twice the amount invested in B. So the equation needs to model "this account is twice that account", not "this sum is twice that sum".

Denis' second line comes by substituting his first line (the "a = 2b") into your first line (the "a + b + c = 8,000"):

. . . . .(a) + b + c = (2b) + b + c = 3b + c = 8,000

...and so forth.

Better?