SOLUTION: Please help me solve this question U r asked by ur elderly neighbour to lay a stone path from the back door of her house to the bird feeder 44 units across her backyard.Each uni

Question 1118352: Please help me solve this question
U r asked by ur elderly neighbour to lay a stone path from the back door of her house to the bird feeder 44 units across her backyard.Each unit is 500mm.she purchased 15 crircular stones,each 1 unit wide in diameter,and would like u to place them equally spaced across the backyard with the last stone touching the feeder.The distance from the house to the first stone is up to you,so you may make it different to the spacing between the stone.Before going to her house to do the work, you have decided to make a plan.
1) how far apart would you lay the stones to use all 15 to reach the bird feeder?
2) How much space would you leave between the house and the first stone?
3) How far will the house be from the near side of the third stone?
4) How far will the house be from the near side of the fifth stone
5) The tenth stone? The fourteenth stone?
6) Describe the method or methods you used to answer number 3-5
7) Build a table to show how far each of the fifteen stones will be from the house. One column would be numbered 1 to 15.
8) The second column would show the distance from the house to the to the first stone, from the house to the second stone, etc.
9) Find an equation that describes the relationship.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

The 44 units from the house to the feeder is made up of
(1) 15 stones, each 1 unit wide;
(2) 14 spaces between stones, each x units wide; and
(3) the space between the house and the first stone, y units wide.

Then

There are of course many solutions to this equation where x and y are positive numbers. But by far the simplest one -- and one which uses a reasonable distance from the house to the first stone -- is x=2 and y=1.

So you could place the first stone 1 unit from the house and then place the stones 2 units apart.

The units in the problem are each 500mm, or 0.5 meters. So this solution has the first stone 0.5 meters from the house and 1 meter between stones.

(It should be noted that 1 meter between stones is quite a large step for the elderly neighbor.)

So we have answers for the first two questions: the stones are 2 units (1m) apart; the first stone is 1 unit (0.5m) from the house.

After that, the questions can be answered in any order. It seems easiest to answer the last question next; all the other questions can be answered using the answer to the last question.

The first stone is 0.5m from the house; from the beginning of each stone to the beginning of the next stone is a distance of 1 unit for the stone and 2 units for the space between stones, for a total of 3 units, or 1.5m.

So the distance from the house to the first stone is 0.5m, and you add 1.5m for each additional stone. Using any of several algebraic methods, you can find the formula for the distance from the house to the n-th stone to be (1.5n-1)m.

Use that formula to answer the other questions.
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