Help I need this answered

Question

  Sarah invested $20 000. Part was invested in an account earning %5 and the rest was in an account earning %8. She earned $1150 in interest. How much money did she invest in each account. Set up the system but do not solve. 

Answer 1

We know that Interest = Principal x Rate x Time

No Time is specified here, so we will assume that Time = 1 year.

Rate will be expressed as a decimal.

 

So, what we have here is that $1150 = Principal 1 x 0.05 + Principal 2 x 0.08. Further, we know that Principal 2 = $22,000 - Principal 1

 

Let x = Principal 1; then $20,000 - x = Principal 2

 

Our equation becomes $1150 = 0.05x + 0.08($20,000 - x)

expanding, we get $1150 = 0.05x + $1600 - 0.08x

combining, we get -$450 = -0.03x

multiply both sides by -1 to get $450 = 0.03x

solving, x = $15000

 

So, Principal 1 = $15000, and Principal 2 = $5000

 

Proof: $15000 x 0.05 + $5000 x 0.08 = $1150

$750 + $400 = $1150