Question

Barbara wants to earn $500 a year by investing $5000 in two
accounts, a savings plan that pays 8% annual interest and a highrisk
option that pays 13.5% interest. How much should she invest
at 8% and how much at 13.5%? Write a system of equations that
would allow you to solve Barbara’s dilemma. Solutions please

Answer 1

assume annual interest  8% as X

assume annual interest 13.5% as Y 

according to the question

X + Y = 5000 ------------------- > 1

 she wants’ to earn in 500 in the both situation 

8/100 = 0.08 X

therefore 8% would be 0.08X

13.5/100=0.135X

therefore 13.5% would be 0.135y

according to equation 1

0.08x + 0.135y = 500

hence proved

Answer 2

We have given that L ∝ h²
So, L = kh² [puting a constant]
Case 1 Arise: 
2000 = k × (5)²
k = 2000/25 
k= 80 

Case 2 Arises: 
L = kh² 
L = 80 × (9)²
L = 80 × 81 
L= 6480 pounds