1. A farmer had several pens out by the barn. He had used 17 lenghts of fence to make the pens, but now he needs to use six of those fence lengths for another project. He wants to remove six fence lenghts but still have two square pens remaing. Which lenghts should he remove?
The equivalent idea is to make two square pens out of 17-6=11 match-sticks. They are attached together.
To solve this question, we need to figure out how many lengths of fence are used for each square pen.
Let's assume each square pen requires "x" lengths of fence.
Since the farmer wants to have two square pens remaining after removing six lengths of fence, the total number of lengths of fence for two square pens would be 2x.
Initially, the farmer used 17 lengths of fence to make all the pens. After removing six lengths of fence, there will be 17 - 6 = 11 lengths of fence remaining.
Now, we can set up an equation to find the value of "x":
2x = 11
To solve for x, we divide both sides of the equation by 2:
x = 11/2
Since the number of lengths of fence must be a whole number, we round up the value of x to the nearest whole number:
x = 6
Therefore, each square pen requires 6 lengths of fence. The farmer should remove 6 lengths of fence from the total of 17 lengths.