Question

A board 24 inches long is cut into two pieces in the ratio 3:5.Find the length of each piece.

Answer 1

The answer would be 9 and 15.
This is because when splitting you could name the two pieces 3x and 5x. You could then add those pieces together (creating 8x) to set it equal to 24 (8x=24). Then solving that equation x=3. You plug x back into the original equations you created so 3x3=9 and 5x3=15.

Answer 2

Step-by-step explanation: Since the two pieces of the board are in the ratio 3:5, we can represent the pieces as 3x and 5x.

So let's call 3x our first piece and 5x our second piece.

Now since we know that the original board is 24 inches long,

our two pieces must add to 24 inches.

So we can setup the equation 3x + 5x = 24.

Simplifying on the left side we have 8x =24.

Now divide both sides by 8 to get x = 3.

So the length of the first piece, 3x, is 3(3) or 9 inches.

The length of the second piece, 5x, is 5(3) or 15 inches.

Finally, make sure to check the answer back in

the original problem to see if it makes sense.

In this case, 9 inches + 15 inches = 24 inches so our answer checks.