Mathematics, 06.10.2019 16:30 shannydouglas

Mr. townes created a 2-foot wide garden path around a circular garden. the radius of the garden is 7 feet. he wants to cover the path in stones. if mr. townes needs 1 bag of stones for every 5 square feet of path, how many bags of stones will he need 5o cover his garden path?

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Answer from: winterblackburn78

The bags of stones Mr. Townes will need are 20 bags.

Given:

The radius of the circular garden is 7 feet.

The width of the circular path around the park is 2 feet.

To find:

The bags of stones needed by Mr. Townes to cover the garden path.

Solution:

The radius of the circular garden = 7 ft

The width of the circular path around the park = 2 ft

The radius of the inner circle = r = 7 ft

The radius of the outer circle = r' = 7 ft + 2 ft = 9 ft

The area of the inner circle = A

$A=\pi r^2\\\\A=3.14\times (7 ft)^2=153.94 ft^2$

The area of the outer circle = A'

$A'=\pi r'^2\\\\A'=3.14\times (9 ft)^2=254.47ft^2$

The area of the circular garden path = C

$C = A' - A \\\\= 254.47ft^2-153.94 ft^2 =100.53ft^2$

Mr. Townes needs 1 bag of stones for every 5 square feet of a path, then for 100.53 square feet he will need:

$=\frac{1}{5}\times 100.53=20.106bags\approx 20bags$

The bags of stones Mr. Townes will need are 20 bags.

Learn more about the unitary method here:

link

Mr. townes created a 2-foot wide garden path around a circular garden. the radius of the garden is 7

Answer from: emilyturchon

See photo for solution
Mr. townes created a 2-foot wide garden path around a circular garden. the radius of the garden is 7

Answer from: Quest

What is the rest of the question?

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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Mr. townes created a 2-foot wide garden path around a circular garden. the radius of the garden is 7...