Question

Candace had $20,000 to invest. She invested part the money at 5% and the remaining part of the money at 8%. If her income from the two investments was $1435, how much did she invest at each of the rates?

a
$5000 at 5% and $15000 at 8%
b
$14500 at 5% and $5500 at 8%
c
$3500 at 5% and $16500 at 8%
d
$5500 at 5% and $14500 at 8%

Answer 1

D

Explanation:

To solve this problem, we can use algebra. Let's call the amount invested at 5% "x" and the amount invested at 8% "y".

We know that:

x + y = $20,000 (because this is the total amount Candace had to invest)

We also know that:

0.05x + 0.08y = $1435 (because this is the total income from the two investments, and we need to use the percentage rates to calculate the income)

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y:

y = $20,000 - x

We can substitute this expression for y into the second equation:

0.05x + 0.08($20,000 - x) = $1435

0.05x + 0.08($20,000) - 0.08x = $1435

0.05x - 0.08x = $1435 - 0.08($20,000)

-0.03x = $1435 - $1600

-0.03x = -$165

x = $5500

So, Candace invested $5500 at 5%. To find how much she invested at 8%, we can use one of the original equations:

x + y = $20,000

$5500 + y = $20,000

y = $20,000 - $5500

y = $14500

Therefore, Candace invested $14500 at 8%

The answer is d) $5500 at 5% and $14500 at 8%