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1.7.2: Working with Ratio Segments

Landscapers will often stake a sapling to strengthen the tree’s root system. A typical method of staking a tree is to tie wires to both sides of the tree and then stake the wires to the ground. If done properly, the two stakes will be the same distance from the tree.

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1.7.2: Working with Ratio Segments

1. Assuming the distance from

the tree trunk to each stake

is equal, what is the value of x?

2. How far is each stake from the tree?

3. Assuming the distance from the tree

trunk to each stake is equal, what is

the value of y?

4. What is the length of the wire from

each stake to the tie on the tree?

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1.7.2: Working with Ratio Segments

2y + 17

7y – 3

4x – 5 2x + 1

1. Assuming the distance from the tree trunk to each stake is equal, what is the value of x?• To find the value of x, set both expressions equal

to each other.

• The value of x is 3.4

1.7.2: Working with Ratio Segments

Set the expressions equal to each other.

Subtract 2x from both sides of the equation.

Add 5 to both sides of the equation.

Divide both sides by 3.

2x = 6

x = 3

4x – 5 = 2x + 1

2x – 5 = 1

2. How far is each stake from the tree?• To determine how far each stake is from the tree,

substitute 3 for x in either expression.

• Each stake is 7 units from the tree trunk.5

1.7.2: Working with Ratio Segments

Original expression

Substitute 3 for x.

Simplify.12 – 5 = 7

4x – 5

4(3) – 5

Original expression

Substitute 3 for x.

Simplify.6 + 1 = 7

2x + 1

2(3) + 1

3. Assuming the distance from the tree trunk to each stake is equal, what is the value of y?• To find the value of y, set both expressions equal

to each other.

• The value of y is 4.6

1.7.2: Working with Ratio Segments

Set the expressions equal to each other.

Subtract 2y from both sides of the equation.

Add 3 to both sides of the equation.

Divide both sides by 5.

20 = 5y

y = 4

2y + 17 = 7y – 3

17 = 5y – 3

4. What is the length of the wire from each stake to the tie on the tree?• To determine the length of the wire from each

stake to the tie on the tree, substitute 4 for y in each expression.

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1.7.2: Working with Ratio Segments

• The length of the wire from each stake to the tie on the tree trunk is 25 units.

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1.7.2: Working with Ratio Segments

Original expression

Substitute 4 for y.

Simplify.8 + 17 = 25

2y + 17

2(4) + 17

Original expression

Substitute 4 for y.

Simplify.28 – 3 = 25

7y – 3

7(4) – 3