A company placed $1,000,000 in three different accounts. It placed part in short term notes paying 4.5% per year, twice as much in government bonds paying 5%, and the rest in utility bonds paying 4%. The income after one year was $45,500. What are the three equations needed to set this problem up? How much did the company pay?

Opps the last question was "How much did the company place in each account?"

To set up this problem, we can use the following three equations:

Let x be the amount placed in short term notes (paying 4.5%)
Let 2x be the amount placed in government bonds (paying 5%)
Let 1,000,000 - x - 2x be the amount placed in utility bonds (paying 4%)

1. The income earned from short term notes: x * 0.045 = 0.045x
2. The income earned from government bonds: (2x) * 0.05 = 0.1x
3. The income earned from utility bonds: (1,000,000 - x - 2x) * 0.04 = (1,000,000 - 3x) * 0.04 = 40,000 - 0.12x

The total income after one year was $45,500, so the sum of the incomes from each type of investment is equal to $45,500:

0.045x + 0.1x + (40,000 - 0.12x) = 45,500

To find the value of x, we can solve this equation.

Now, let's solve it:

Combine like terms:
0.045x + 0.1x + 40,000 - 0.12x = 45,500
0.025x + 40,000 = 45,500

Subtract 40,000 from both sides:
0.025x = 5,500

Divide both sides by 0.025:
x = 220,000

So, the company placed $220,000 in short term notes (paying 4.5%), $440,000 in government bonds (paying 5%), and the remaining amount, $340,000, in utility bonds (paying 4%).

Therefore, the company paid a total of $1,000,000.