SOLUTION: Mr. Rich invested 50,000. Part of it he put in a gold mine stock from which he hoped to receive 20% per year. The rest he invested in bank stock which was paying 6%. If he received

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Mr. Rich invested 50,000. Part of it he put in a gold mine stock from which he hoped to receive 20% per year. The rest he invested in bank stock which was paying 6%. If he received      Log On


   

Question 104921: Mr. Rich invested 50,000. Part of it he put in a gold mine stock from which he hoped to receive 20% per year. The rest he invested in bank stock which was paying 6%. If he received 400 more the first year from the bank stock than from the mining stock, how much did he invest in each stock?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's name the variables first
G-amount of money he put in the gold stock
B-amount of money he put in the back stock
1.G%2BB=50000
Interest for one year is calculated using the rate and the amount of money.
I%5BG%5D=G%2A20%2F100 Interest for gold stock
I%5BB%5D=B%2A6%2F100 Interest for bank stock
You also know a relationship between the interests from each stock.
I%5BB%5D=I%5BG%5D%2B400Interest between gold stock and bank stock
B%2A6%2F100=G%2A20%2F100%2B400Susbtitute.
2.6B=20G%2B40000 Multiply by 100 to simplify.
From equation 1,
G%2BB=50000
B=50000-G
Substituting into 2,
6B=20G%2B40000
6%2850000-G%29=20G%2B40000Substitute.
300000-6G=20G%2B40000Distribute.
260000=26G
G=10000
From 1,
B=50000-G
B=50000-10000Substitute.
B=40000
Check your answer.
B%2A6%2F100=G%2A20%2F100%2B400
40000%2A6%2F100=10000%2A20%2F100%2B400
2400=2000%2B400
2400=2400
Good answer.