A 64 inch long board is divided into lengths in the ratio 2:3. What are the two lengths into which the board is divided? Thanks

let x = length of the first

let 64 - x = length of the second
since they are in ration 2:3, we can write this as:
2/3 = x/(64-x)
cross-multiplying, we have:
2(64-x) = 3x
128 - 2x = 3x
128 = 5x
x = 25.6 inches
64-x = 38.4 inches

hope this helps~ :)

To find the two lengths into which the board is divided, we need to use the given ratio of 2:3.

Step 1: Calculate the total number of parts in the ratio by adding the two numbers together: 2 + 3 = 5.

Step 2: Divide the total length of the board by the total number of parts: 64 inches / 5 = 12.8 inches.

Step 3: Multiply the length of each part by the respective part of the ratio:

- Multiply the first part of the ratio (2) by the calculated length of each part (12.8 inches):
2 * 12.8 = 25.6 inches.

- Multiply the second part of the ratio (3) by the calculated length of each part (12.8 inches):
3 * 12.8 = 38.4 inches.

Therefore, the two lengths into which the board is divided are 25.6 inches and 38.4 inches.

To find the two lengths into which the 64-inch long board is divided in the ratio 2:3, we can follow these steps:

Step 1: Add the two parts of the ratio (2 + 3 = 5). This represents the total number of parts that the ratio is divided into.

Step 2: Divide the total length of the board by the total number of parts. In this case, the total length is 64 inches, and the total number of parts is 5. Therefore, dividing 64 by 5 gives us the value of each part.

64 / 5 = 12.8

Step 3: Multiply the value of each part by the corresponding ratio value to get the actual lengths. In this case, the ratio is 2:3, so multiplying 12.8 by 2 gives us the length of the first part, and multiplying 12.8 by 3 gives us the length of the second part.

Length of the first part: 12.8 * 2 = 25.6 inches
Length of the second part: 12.8 * 3 = 38.4 inches

Therefore, the two lengths into which the 64-inch long board is divided in the ratio 2:3 are 25.6 inches and 38.4 inches.