Question 86956

Interest(I)=Principal(P) times Rate(R) times Time(T) (note: in this problem, T=1 year)

Let P=amount invested at 5%
Interest at 5%=P(0.05)(1)=0.05P

Then 50,000-P=amount invested at 4%
Interest at 4%=(50,000-P)(0.04)(1)=(0.04)(50,000-P)

Now we are told that the interest earned at 5%((0.05)(P)) plus the interest earned at 4%((0.04)(50,000-P)) equals $2100. So, our equation to solve is:

0.05(P)+0.04(50,000-P)=2100  get rid of parens

0.05P+2000-0.04P=2100  subtract 2000 from each side

0.05P+2000-2000-0.04P=2100-2000 collect like terms

0.01P=100  divide both sides by 0.01

P=$10,000-----------------------------------amount invested at 5%

50,000-P=50,000-10,000=$40,000--------------amount invested at 4%

CK

0.05*10,000+0.04*40,000=2100

500+1600=2100
2100=2100


Hope this helps---ptaylor