Solve the problem.

-Roberto invested some money at 6%, and then invested $2000 more than twice this amount at 10%. His total annual income from the two investments was $3840. How much was invested at 10%?
A) $3000
B) $28,000
C) $30,000
D) $6000

Question

Solve the problem.

-Roberto invested some money at 6%, and then invested $2000 more than twice this amount at 10%. His total annual income from the two investments was $3840. How much was invested at 10%?
A) $3000
B) $28,000
C) $30,000
D) $6000

Quizplus · Accepted Answer

Let x be the amount invested at 6%.
Then the amount invested at 10% is 2x+2000.

The income from the 6% investment is:

0.06x

The income from the 10% investment is:

0.1(2x+2000)

The problem tells us that the total income is $3840, so we have the equation:

0.06x + 0.1(2x+2000) = 3840

Simplifying:

0.06x + 0.2x + 200 = 384

0.26x = 3680

x = 14230.77 (rounded to two decimal places)

So, the amount invested at 10% is:

2x+2000 = 2(14230.77)+2000 = 30461.54

Therefore, the answer is C: $30,000.

Solve the Problem. -Roberto Invested Some Money at 6%, and Then Invested $2000