The Smiths invested $14,000, part at 3% simple interest and the rest at 4% simple interest for a period of one year. if the total interest earned was $460, how much was invested at each rate?

One gallon of paint covers an area of 400 square feet. Write an expression that can be

used to calculate the number of gallons of paint the farmer will need to buy to paint the
shaded regions of the storage building and the shaded region of the grain silo.

To find out how much the Smiths invested at each rate, let's break down the problem into two equations.

Let's assume that the amount invested at 3% is x dollars.
Therefore, the amount invested at 4% would be (14,000 - x) dollars (since the total investment is $14,000).

Now, let's calculate the interest earned on each investment:

Interest earned at 3% = (x) * (0.03) * (1) = 0.03x dollars
Interest earned at 4% = (14,000 - x) * (0.04) * (1) = 0.04(14,000 - x) dollars

Since the total interest earned is $460, we can set up the following equation:

0.03x + 0.04(14,000 - x) = 460

Let's solve the equation step by step:

0.03x + 0.04(14,000 - x) = 460
0.03x + 560 - 0.04x = 460
-0.01x = -100
x = -100 / -0.01
x = 10,000

So, the Smiths invested $10,000 at 3% and $4,000 (14,000 - 10,000) at 4%.