Translate to a system of equations and solve.

Question

Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received $5,200 in interest in one year?

Answer 1

a + b = 64,000 -------> a = 64,000 - b

0.055a + 0.09b = 5200

 

0.055(64,000 - b) + 0.09b = 5200

 

Solve for b, then plug your answer into the first equation to find a.

Answer 2

Invested $64000, $x at rate 5.5%, remaining $y at rate 9%

x+y=6400

0.055 x + 0.09 y = 5200,

 x=16,000

y=48000.

 

or just solve

 

0.055 x + 0.09 (64000 - x) = 5200,
x=16,000