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Scrat [10]
3 years ago
13

Challenge: How many flowers, spaced every 4 in., are needed to surround a circular garden with a

Mathematics
1 answer:
meriva3 years ago
6 0

Answer:

314 flowers

Step-by-step explanation:

In order to find how long the perimeter of the circular garden is, we need to find the circumference of the garden.

The circumference of a circle is radius*2*pi. So, in this case, the circumference would be 200*2*3.14. This equals 1256 inches.

Next, we know that flowers are planted every 4 inches, so all we need to do is to find how many 4-inch segments are in 1256 inches.

1256/4=314

Thus, 314 flowers are needed.

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Let x be the number of weeks; therefore, the two linear equations are

\begin{gathered} T=2+7x \\ \text{and} \\ C=11+4x \end{gathered}

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\begin{gathered} T=C \\ \Rightarrow2+7x=11+4x \\ \Rightarrow3x=9 \\ \Rightarrow x=\frac{9}{3}=3 \\ \Rightarrow x=3 \end{gathered}

Thus, substitute the value of x=3 into the first equation,

\begin{gathered} x=3 \\ \Rightarrow T=2+7\cdot3=23 \\ \Rightarrow T=23 \end{gathered}

Thus, after 3 weeks, Josiah will have the same number of punches on each card, and he will have 23 punches on each card.

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