For that problem: A board that is 12 feet long must be cut into 2 pieces that have lengths in a ratio of 3 to 2. Find the lengths of the two pieces.
when answering the question why was it 3/5=x/12? where did the 5 come from?
With a ratio of 3:2, your total is 5. You're figuring 3 parts of 5.
but arn't you figuring 2 parts because its cut in two??
Please read my explanation.
http://www.jiskha.com/display.cgi?id=1298850580
To find the lengths of the two pieces of the board, we can set up a proportion based on the given ratio. The ratio is 3 to 2, which means that one part is 3 and the other part is 2.
Let's assume the length of the first piece is x. So, the length of the second piece will be (12 - x), as the total length of the board is 12 feet.
To set up the proportion, we compare the ratio of the two lengths to the ratio of the two parts:
3/2 = x/(12 - x)
Now, you asked where the 5 in 3/5 = x/12 came from. It seems there might be a mistake in the equation you provided. The correct equation for this problem should be 3/2 = x/(12 - x).
We got 12 - x in the denominator because the two lengths add up to the total length of the board, which is 12 feet.
To solve this equation and find the value of x, we can cross-multiply:
3(12 - x) = 2x
Simplifying further:
36 - 3x = 2x
2x + 3x = 36
5x = 36
x = 36/5
x ≈ 7.2
So, the length of the first piece is approximately 7.2 feet, and the length of the second piece would be approximately 12 - 7.2 = 4.8 feet.