Question

A woman invested 4 times as much as 5% as she did at 6%. The total amount of interest she earns is 1 year from both accounts is $520 . How much did she invest at each rate?

Answer 1

at 5% interest, she invested $8,000

at 6% interest, she invested $2,000

Explanation:

Let the invested amount at 5% interest = x

Let the invested amount at 6% interest = y

x = 4y - - - - (1) (A woman invested 4 times as much as 5% as she did at 6%)

5% of x = 0.05x

6% of y = 0.06y

0.05x + 0.06y = 520 - - - - (2) (The total amount of interest she earns is $520)

putting the value of x gotten in equation (1) into eqn (2):

0.05x + 0.06y = 520

where x = 4y

∴ 0.05(4y) + 0.06y = 520

0.2y + 0.06y = 520

0.26y = 520

y = 520 ÷ 0.26

y = $2000

from eqn (1)

x = 4y

since y = 2000

x = 4 × 2000

x = $8000