QuestionA lady has 4 gold chains with 3 links each. Can she join them for less than 4\$? How many cuts for 5 chains?
Studdy Solution
STEP 1
Assumptions1. Each piece of gold chain contains three links.
. The jeweler charges a dollar for each link which is cut open and welded together again.
3. The goal is to minimize the cost of joining the chains together.
STEP 2
For the first part of the problem, we need to find a way to join the four pieces of chain together with fewer than four cuts.
STEP 3
We can do this by taking one piece of chain and cutting all three of its links. This will give us three separate links.
STEP 4
We can then use these three separate links to join the other three pieces of chain together. This requires only three cuts, not four.
STEP 5
So, for the first part of the problem, the lady can have the chains joined together for3 dollars, not4.
STEP 6
For the second part of the problem, we need to find the smallest number of links that must be cut and welded to make a complete bracelet from five pieces of chain.
STEP 7
We can use a similar strategy as in the first part of the problem. We take one piece of chain and cut all three of its links.
STEP 8
We can then use these three separate links to join the other four pieces of chain together. This requires three cuts.
STEP 9
However, we still have one piece of chain left. We need to cut one link from this chain and use it to join the chain to the rest of the bracelet.
STEP 10
So, for the second part of the problem, the smallest number of links that must be cut and welded to make a complete bracelet from five pieces of chain is4.
The solutions to the problems area) The lady can have the chains joined together for3 dollars, not4.
b) The smallest number of links that must be cut and welded to make a complete bracelet from five pieces of chain is4.
Was this helpful?
