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Barbara invests $2,400 in the National Bank at 5%. How much additiona

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Barbara invests $2,400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?

(A) $2,400

(B) $3,600

(C) $1,000

(D) $3,000

(E) $1,200

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Re: Barbara invests $2,400 in the National Bank at 5%. How much additiona  [#permalink]

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New post 05 Mar 2018, 20:43
Bunuel wrote:
Barbara invests $2,400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?

(A) $2,400

(B) $3,600

(C) $1,000

(D) $3,000

(E) $1,200


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Barbara invests $2,400 in the National Bank at 5%. How much additiona  [#permalink]

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New post 05 Mar 2018, 22:40
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Bunuel wrote:
Barbara invests $2,400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?

(A) $2,400

(B) $3,600

(C) $1,000

(D) $3,000

(E) $1,200


If the interest earned is represented as follows
5-----------8
------6------
2-----------1

the investment must be done in the ratio 2:1

Therefore, we would need to invest $1200(Option E) at a rate of 8% so that the total annual income is 6%

Alternate approach


Let x be the amount invested at 8%

\(0.05*2400 + 0.08*x = 0.06(2400 + x)\) -> \(120 + 0.08x = 144 + 0.06x\) -> \(0.02x = 24\) -> \(x = \frac{2400}{2} = $1200\)
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Re: Barbara invests $2,400 in the National Bank at 5%. How much additiona  [#permalink]

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New post 06 Mar 2018, 00:59
Bunuel wrote:
Barbara invests $2,400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?

(A) $2,400

(B) $3,600

(C) $1,000

(D) $3,000

(E) $1,200


We need to have the equation as follows.
Additional money=x
Therefore, (6/100)*x+144=120+(8/100)*x
Solving for x, x=1200
Answer E
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Re: Barbara invests $2,400 in the National Bank at 5%. How much additiona  [#permalink]

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New post 08 Mar 2018, 10:37
Bunuel wrote:
Barbara invests $2,400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?

(A) $2,400

(B) $3,600

(C) $1,000

(D) $3,000

(E) $1,200


We can let x = the amount of money invested at 8%, making her entire investment equal to (2,400 + x). We can create the following equation:

0.05(2,400) + 0.08x = 0.06(2,400 + x)

120 + 0.08x = 144 + 0.06x

0.02x = 24

2x = 2400

x = 1,200

Answer: E
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Re: Barbara invests $2,400 in the National Bank at 5%. How much additiona  [#permalink]

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New post 04 Oct 2018, 18:25
Hi All,

We're told that Barbara invests $2400 in the National Bank at 5%. We're asked how much additional money she must invest at 8% so that the TOTAL annual income will be equal to 6% of her TOTAL investment. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.

To start, the $2400 invested at 5% would earn ($2400)(.05) = $120.

Since Barbara invested $2400 at 5%, IF she were to invest another $2400 at 7%, then the average return for the total investment would be exactly 6% (since the EQUAL investments at 5% and 7% would 'average out' to 6%. Here though, she's investing money at 8% - which means that she would NOT need $2400 invested there (she would need LESS than that, since the investment is at a higher rate). Thus, the answers are narrowed down to either $1000 or $1200. It's interesting that one of the two options is EXACTLY HALF of 2400....

Let's TEST Answer E = $1200
IF... $1200 were invested at 8%, then
that investments would earn (1200)(.08) = $96
the total money invested would equal $2400 + $1200 = $3600
the total return on the investment would be $120 + $96 = $216

1% of $3600 = $36
6% of $3600 = $216
This is an exact match for what we were told, so this MUST be the answer.

Final Answer:

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Re: Barbara invests $2,400 in the National Bank at 5%. How much additiona  [#permalink]

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New post 27 Jan 2019, 05:44
Bunuel wrote:
Barbara invests $2,400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?

(A) $2,400

(B) $3,600

(C) $1,000

(D) $3,000

(E) $1,200

Let´s use ALLIGATION, one powerful technique covered in our course!

Image


\(? = x\)


\({{2400} \over {2400 + x}} = {{8 - 6} \over {8 - 5}} = {{2 \cdot 1200} \over {3 \cdot 1200}}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 3 \cdot 1200 - 2400 = 1200\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Barbara invests $2,400 in the National Bank at 5%. How much additiona  [#permalink]

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New post 27 Jan 2019, 06:13
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Bunuel wrote:
Barbara invests $2,400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 6% of her entire investment?

(A) $2,400

(B) $3,600

(C) $1,000

(D) $3,000

(E) $1,200


Barbara invests $2400 in the National Bank at 5%.
So, her annual income for this investment = 5% of $2400 = $120
Let x = the additional money Barbara must invest at 8%
So, her annual income for this investment = 8% of x = 0.08x
So, Barbara's TOTAL annual income = $120 + 0.08x

We want the TOTAL annual income to be equal to 6% of her entire investment.
The TOTAL amount invested = $2400 + x
So, we want her TOTAL annual income to equal 6% of ($2400 + x)
In other words, we want: Barbara's TOTAL annual income = 0.06($2400 + x)

We now have the equation: $120 + 0.08x = 0.06($2400 + x)
Expand right side: 120 + 0.08x = 144 + 0.06x
Subtract 0.06x from both sides to get: 120 + 0.02x = 144
Subtract 120 from both sides to get: 0.02x = 24
Solve: x = 24/0.02 = 2400/2 = 1200

Answer: A

Cheers,
Brent
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Re: Barbara invests $2,400 in the National Bank at 5%. How much additiona   [#permalink] 27 Jan 2019, 06:13
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