Question

Jenny receives $1,270 per year from three different investments totaling $20,000. One of the investments pays 6%, the second one pays 8%, and the third pays 5%. If the money invested at 8% is $1,500 less than the amount invested at 5%, how μch money has Jenny invested in all three investments?

a) $17,000

b) $18,500

c) $19,000

d) $20,000

Answer 1

Jenny has invested $11,909.09 at 5%, $10,409.09 at 8%, and $7,681.82 at 6%. So, she has invested a total of $30,000. Therefore, the correct option is d) $20,000.

Step-by-step explanation:

Let's solve this problem step by step:

1. Let's assume the amount invested at 5% is x. So, the amount invested at 8% would be x - $1,500.
2. Now, we can set up the equation: x * 0.05 + (x - $1,500) * 0.08 + (20,000 - x - (x - $1,500))) * 0.06 = $1,270
3. Simplifying the equation, we get 0.05x + 0.08(x - $1,500) + 0.06(20,000 - x - (x - $1,500))) = $1,270
4. Distributing and simplifying further, we get 0.05x + 0.08x - $120 + 0.12(20,000 - 2x + $1,500) = $1,270
5. Combining like terms, we get 0.13x + 240 + 0.12(21,500 - 2x) = $1,270
6. Further simplifying, we get 0.13x + 2,580 - 0.24x = $1,270
7. Combining like terms, we get -0.11x + 2,580 = $1,270
8. Subtracting $2,580 from both sides, we get -0.11x = - $1,310
9. Dividing both sides by -0.11, we get x = $11,909.09

Jenny has invested $11,909.09 at 5%, $10,409.09 at 8%, and $7,681.82 at 6%. So, she has invested a total of $11,909.09 + $10,409.09 + $7,681.82 = $30,000. Therefore, the correct option is d) $20,000.