I need serious help with a couple of word problems

Question

Pat invested a total of $3,000. Part of the money was invested in a money market account that paid 10% simple annual interest, and the remainder of the money was invested in a fund that paid 8% simple annual interest. If the total interest earned at the end of the first year from these investments was $256, how much did Pat invest at 10% and how much at 8%?

Answer 1

Let X be the amount invested at 10% and Y be the amount invested at 8%

10% = 0.10 and 8% = 0.08

 

X + Y = 3000  ---> Y = 3000 - X

 

0.10X + 0.08Y = 256

 

0.10X + 0.08 ( 3000 - X) = 256

 

0.10X + 0.08*3000 - 0.08X = 256

 

0.02X + 240 = 256

 

0.02X = 16

 

2X = 1600

 

X=800

 

y = 3000 - 800 = 2200

 

10% of 800 + 8% of 2200 = 80 + 176 = 256

 

He invested $800 at 10% and $2200 at 8%