Final answer:
To find the lengths of the two pieces of the stick with a total length of 3 feet and a ratio of 5:7, we set up and solved a proportion. We found x = 0.25 feet and then calculated each piece to be 1.25 feet and 1.75 feet long respectively.
Step-by-step explanation:
We need to find the lengths of the two pieces of the stick that are in the ratio of 5:7 and the total length of the stick is 3 feet. To solve this, we'll use the concept of proportions. First, let's represent the length of the shorter piece as 5x and the longer piece as 7x. The sum of these two pieces is equal to the total length of the stick, which is 3 feet.
So, you'll have the equation 5x + 7x = 3. Combining like terms gives us 12x = 3. Dividing both sides by 12 gives us x = 3/12, which simplifies to x = 1/4 or 0.25 feet. Now we simply multiply x by the ratios given to find the length of each piece.
For the shorter piece: 5x = 5 * 0.25 = 1.25 feet.
For the longer piece: 7x = 7 * 0.25 = 1.75 feet.
So the two pieces of the stick are 1.25 feet and 1.75 feet long, respectively.