Chapter 3.3, Problem 64PPE

To determine

To find: The minimum number of pavers to make the walkway.

Answer to Problem 64PPE

The least number of pavers $\text{263}$ .

Explanation of Solution

Given information:

Dimension of rectangular walkway $3\frac{1}{3}$ ft, i.e. $\frac{10}{3}$ ft wide by 35 ft long using square cement pavers.

Each paver has an area $\frac{4}{9}{\text{ft}}^2$ .

Calculation:

Let the length of each paver is $x$ ft. Also, each paver is also $\frac{10}{3}$ wide. According to the problem, $\frac{10}{3}x=\frac{4}{9}.$ Now,

  $\frac{10}{3}x=\frac{4}{9}$

  $\cancel{\frac{3}{10}}\times \cancel{\frac{10}{3}}x=\frac{3}{10}\times \frac{4}{9}\left(\text{multiply each side by}\frac{3}{10}\right)$

  $x=\frac{2}{15}$ (simplify)

The walkway is $35\text{ft}$ long. Let $y$ represents the number of pavers with length $\frac{2}{15}\text{ft}$ for $35\text{ft}$ long walkway. Then the problem can be modeled as: Length of each paver times number of papers is at least length of walkway. Then $\frac{2}{15}y\ge 35.$

Now,

  $\frac{2}{15}y\ge 35$

  $\cancel{\frac{15}{2}}\times \cancel{\frac{2}{15}}y\ge \frac{15}{2}\times 35\left(\text{multiply each side by}\frac{15}{2}\right)$

  $y\ge \mathrm{262.5.}($ simplify $)$

Since the number of pavers is whole number, the least number of pavers is next positive integer of $262.5\text{ i}\text{.e 263}$ .

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