SOLUTION: A construction worker is building a straight walking path that is 5m long from a client's front door to the sidewalk. The path is to be built out of planks that are 60 cm, 70cm, an
Algebra.Com
Question 767124: A construction worker is building a straight walking path that is 5m long from a client's front door to the sidewalk. The path is to be built out of planks that are 60 cm, 70cm, and 100 cm in length. How many different paths could be constructed using these plank lengths?
My friend asked me this question but I have no idea where to start.I think it will have something to do with combinations but im not sure. Thanks for the help.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The only way to do this is to start with one of the lengths and see what is possible. You have to go 5 meters which is 500 cm, so
9 times 60 is 540. 9 60s is too many,
8 times 60 is 480. You don't have a 20 cm piece, so this doesn't work
7 times 60 is 420. No way to make 80 out of 70 and 100, so this doesn't work.
6 times 60 is 360. 500 minus 360 is 140 which you can make with two 70s.
5 times 60 is 300. 500 minus 300 is 200 which you can make with two 100s.
4 times 60 is 240. No way to get to 260 with just 70s and 100s, so this doesn't work.
3 times 60 is 180. Leaves 320, and you can't get there from here either without using 60s and that possibility is already counted above.
2 times 60 is 120. Leaves 380. 4 70s is 280 plus one 100 makes 380.
1 times 60 is 60. Leaves 440. 2 times 70 is 140 plus 3 times 100.
0 times 60. Leaves 500 which is just five 100s.
In sum:
5 100s
3 100s plus 2 70s plus 1 60
1 100 plus 4 70s plus 2 60s
2 100s plus 5 60s
2 70s plus 6 60s
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
John walks the 15 meters from the front door of his house to his moped at
a constant... (answered by TP)
Santiago is walking to school, which is straight down the road 500m from his home. He... (answered by Edwin McCravy)
Hi there, I have been trying to tackle this homework question for a long time, it would... (answered by stanbon)
You need to build a ramp to a door that is 6ft above ground. If your ramp will extend the (answered by Alan3354)
A building is 2 feet from a 9-foot fence that surrounds the property. A worker wants to... (answered by stanbon)
A building is 1 feet from a 9-foot fence that surrounds the property. A worker wants to... (answered by MathLover1)
A man standing on the roof of a building 65.0 feet high looks down to the building next... (answered by josgarithmetic)
A man standing on the roof of a building 65.0 feet high looks down to the building next... (answered by josgarithmetic)
A man standing on the roof of a building 65.0 feet high looks down to the building next... (answered by Theo)
