Math Word Problem

Question

Pierre inherited $471,000 from his uncle and decided to invest the money. He put part of the money in a money market account that earns 3.5% simple interest. The remaining money was invested in a stock that returned 4% in the first year and a mutual fund that lost 3% in the first year. He invested $10,000 more in the stock than in the mutual fund, and his net gain for 1 yr was $2780.Determine the amount invested in each account.

Answer 1

Let x = market account

Let s = stock account

Let m = mutual account

Now, we know that x + s + m = 471000 and m = s - 10000 or x + s + s - 10000 = 471000

Also,

Interest of x + interest of s + interest of m = 2780

(1.035x - x) + 0.04s - 0.03m=2780

0.035x + 0.04s - 0.03 (s-10000) = 2780

0.035x + 0.04s - 0.03s + 300 = 2780

0.035x + 0.01s = 2480 or

3.5x + s = 248000 (1)

But,

x + s + s - 10000 = 471000 or x + 2s = 481000 (2)

Now we solve equation (1) and (2)

3.5x + s = 248000 (1)

x + 2s = 481000 (2)

-7x - 2s = -496000 (3)

x+2s = 481000 (4)

Add equation (3) and (4)

-6x = -15000 or x = 2500 and 2s = 481000-2500 = 478500 or s = 239250

Hence;

x = 2500, s = 239250 and m = 229250