Final answer:
Dan will make two jump ropes, one 5 feet long and the other 7 feet long, from 12 feet of rope, with the longer rope being 2 feet longer than the shorter one.
Step-by-step explanation:
To solve the problem of how long the two jump ropes are going to be, we can set up an equation. Let's call the length of the shorter piece x feet. Therefore, the length of the longer piece will be x + 2 feet. Since Dan plans to make 2 jump ropes out of 12 feet of rope, the total length of the two pieces together will be 12 feet.
The equation to represent this situation is: x + (x + 2) = 12. Simplifying the equation, we get 2x + 2 = 12. Subtracting 2 from both sides gives us 2x = 10 and dividing both sides by 2 gives us x = 5.
So, the length of the shorter jump rope is 5 feet, and the length of the longer jump rope is 5 + 2, which is 7 feet. Together, they add up to 12 feet, utilizing the entire length of rope Dan has.