A board 20 feet long is cut into two boards with lengths in ratio of 5 to 2. To the nearest tenth of a foot, how lng is the longer piece of the board?

Ratio 5 : 2

5x + 2x = 20

Solve for x.

x=20/7

To find the length of the longer piece of the board, we first need to determine the ratio between the two lengths.

Let's assign variables to the lengths of the two boards. Let x represent the length of the shorter board, and y represent the length of the longer board.

According to the problem, the lengths are in a ratio of 5 to 2. This can be written as:

x/y = 5/2

Now we can set up an equation using the ratio and solve for y (the length of the longer board).

x/y = 5/2

Cross multiplying, we get:

2x = 5y

To isolate y, we divide both sides of the equation by 5:

(2x)/5 = y

Now we can substitute the given information into the equation to find the length of the longer piece.

Since the sum of the two lengths is 20 feet, we have:

x + y = 20

Let's solve this system of equations:

2x = 5y (equation 1)
x + y = 20 (equation 2)

From equation 2, we can solve for x:

x = 20 - y

Substitute this value of x into equation 1:

2(20 - y) = 5y
40 - 2y = 5y

Combine like terms:

7y = 40

Now, divide both sides by 7:

y = 40/7

To the nearest tenth of a foot, the length of the longer piece of the board is approximately:

y ≈ 5.7 feet