MHB Solving an Investment Word Problem

[Elissa89]

So I have an investment word problem that I have tried multiple times and have not been able to get the right answer.

"If Ben invests $4500 at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives is 4.5% of the total amount invested?

Here's my set up:

x= unknown amount invested
y=total amount invested

4500+y=x
4500(.04)+.055=.045y

I then solved for the variables and it was incorrect.

Help please.

 

[S.G. Janssens]

Re: Word investment problem

Are you sure the $x$ and $y$ in your first equation are in the right place?
Also, there seems to be an $x$ missing in the second equation.

 

[Elissa89]

Re: Word investment problem

Are you sure the $x$ and $y$ in your first equation are in the right place?
Also, there seems to be an $x$ missing in the second equation.

I have no idea lol, the setup is what I came up with, we were just given the word problem. So I know my setup is wrong, but I don't know why or how to set it up correctly.

 

[I like Serena]

Re: Word investment problem

I have no idea lol, the setup is what I came up with, we were just given the word problem. So I know my setup is wrong, but I don't know why or how to set it up correctly.

Hi Elissa89! (Wave)

We have:

4500 + unknown additional amount invested = total amount invested
4500 (0.04) + (unknown additional amount invested) (0.055) = (total amount invested) (0.045)
​

don't we?

With your x and y, doesn't that become:

4500 + x = y
4500 (.04) + .055 x = .045 y
​

which is what Krylov was pointing out?

Can you solve that system?

 

[Elissa89]

Re: Word investment problem

Hi Elissa89! (Wave)

We have:

4500 + unknown additional amount invested = total amount invested
4500 (0.04) + (unknown additional amount invested) (0.055) = (total amount invested) (0.045)
​

don't we?

With your x and y, doesn't that become:

4500 + x = y
4500 (.04) + .055 x = .045 y
​

which is what Krylov was pointing out?

Can you solve that system?

I got 6700 for total amount invested and 2200 for unknown additional amount and it's still saying it's incorrect (online homework program)

 

[Elissa89]

Re: Word investment problem

Could someone maybe try it and see what they get?

 

[MarkFL]

Re: Word investment problem

I would let $I$ be the unknown investment amount, and $T$ be the total amount invested, and from the information provided in the problem, we may state:

$$4500+I=T$$

$$.04\cdot4500+.055I=.045T$$

Substitute for $T$ from the first equation into the second, so that we can solve for $I$:

$$.04\cdot4500+.055I=.045(4500+I)$$

Multiply through by 1000:

$$40\cdot4500+55I=45(4500+I)$$

Divide through by 5:

$$8\cdot4500+11I=9(4500+I)$$

Distribute on the RHS:

$$8\cdot4500+11I=9\cdot4500+9I$$

Collect like terms:

$$2I=4500$$

Divide through by 2:

$$I=2250$$

 

[Elissa89]

Re: Word investment problem

I would let $I$ be the unknown investment amount, and $T$ be the total amount invested, and from the information provided in the problem, we may state:

$$4500+I=T$$

$$.04\cdot4500+.055I=.045T$$

Substitute for $T$ from the first equation into the second, so that we can solve for $I$:

$$.04\cdot4500+.055I=.045(4500+I)$$

Multiply through by 1000:

$$40\cdot4500+55I=45(4500+I)$$

Divide through by 5:

$$8\cdot4500+11I=9(4500+I)$$

Distribute on the RHS:

$$8\cdot4500+11I=9\cdot4500+9I$$

Collect like terms:

$$2I=4500$$

Divide through by 2:

$$I=2250$$

Ooooh...ok I see what I did wrong. Thank you!