Word Problem Issues

Question

Tammy invested her savings in two investment funds. The $20,000 that she invested in Fund A returned a 3% profit. The amount that she invested in Fund B returned a 10% profit. How much did she invest in Fund B, if both funds together returned a 5% profit?

Answer 1

Hi Kristina,

Let's write down everything the word problem gives us in a "mathy" way:

1. First, let's call b the amount she invested in Fund B.
2. We are told that Fund A returns a 3% profit. How do we express this mathematically? If a fund returns 3%, that means that the profit is 3% of the investment:
3. Profit from Fund A = $20,000 * 3% = $20,000 * 0.03 = $600
4. We're told that Fund B returns a 10% profit. So, mathematically, we say:
5. Profit from Fund B = money invested in B * 10% = b*0.10
6. We're told that the total profit is 5% of the total investment so, mathematically, we have:
7. Profit from both funds = money invested in both * 0.05 = ($20,000 + b)*0.05

But of course, profit from both funds = Profit from Fund A + Profit from Fund B so if we substitute in the expressions we got in points 2, 3, and 4 we get:

($20,000 + b)*0.05 = $600 + b*0.10

Great, now we have one simple equation to solve for b. Collecting like terms, we get:

$1000 + b*0.05 = $600 +b*0.10

$1000 - $600 = b*.10 - b*0.05

$400 = b*0.05

b = $400 / 0.05

b = $8,000

Hope that helps! Let me know if you have any questions about this solution. :-)

Answer 2

Percent Gained= Profit Amount ($)/ Initial amount ($)

%_X = (X)/ P_x

Or

Profit Amount = Initial investment(Percent Gained)

example: P_x = (X)%_X ; where X is a specific Fund type

Terms:

A - Fund A initial investment

P_A - Profit amount from Fund A

%_A - Percent gained from Fund A: (3%

P_A = (A)%_A

B - Fund B initial investment

P_B - Profit amount from Fund B

%_A - Percent gained from Fund B; (10%)

P_A = (B)%_B

T_A+B - Total Amount Invested: (T_A+B = A + B)

P_A+B - Profit from both P_A+P_B: (P_A+B = P_A+P_B)

%_A+B - Percent gained from both P_A+P_B; (5%)

P_A+B = (T_A+B )%_A+B

Givens:

A = $20,000

%_A = 3%

B = ?

%_b = 10%

%_A+B = 5%

Note: you can't just add up 3% + 10% and magically get 5% that maybe where you are getting stuck.

The key is to understand the profit equation for each fund and profit for the total funds.

You don't need to know what the Profit of fund B (P_B) is because you can represent it in terms of B.

Step 1:

Solve or simplify any equations you can.

P_A = (A)%_A

P_A = (.03)A

P_A = (.03)($20,000)

P_A = $600

P_B = (B)%_B

P_B = .10B

Note: sometimes it was easier for me to think about the % as the total gained divided by the total invested

P_A+B = (T_A+B )%_A+B [P_A+B = P_A+P_B; T_A+B = A + B ; %_A+B = 5%]

P_A+P_B = .05 (A + B) [P_A = (.03)A; P_B = .10B]

.03A + .10B = .05A +. 05B

- .03A -.05B -.03A -.05B

.05B = .02A

B = (.02/.05) A

B = .04 A [A = $20,000]

B = .04 A

B = $8,000

P_B = .10B

P_B = .10($8000)

P_B = $800

Answer Tammy Invested $8000 into Fund B

Check Your Answer

P_A+B = (T_A+B )%_A+B

%_{A+B =} P_A+B/(T_A+B )

%_A+B = ($600 + $800)/($20,000 + $8000 )

%_A+B = ($1400)/($28,000)

%_A+B = .05 => 5% It's Good!