Questions: A chain-saw rental firm charges 26 per day or fraction of a day to rent a saw, plus a fixed fee of 8 for re-sharpening the blade. Additional portions of a day are considered to a be a full day's rental, so rounding upward to identify an entire rental period may be necessary. Let S(x) represent the cost of renting a saw for x days. Complete parts (a) through (m) below. (c) Find S(1 1/10). S(1 1/10)=60 (d) Find S(3 1/4). S(3 1/4)=112 (e) Find S(5). S(5)=138 (f) Find S(5 1/5). s(5 1/5)=

A chain-saw rental firm charges 26 per day or fraction of a day to rent a saw, plus a fixed fee of 8 for re-sharpening the blade. Additional portions of a day are considered to a be a full day's rental, so rounding upward to identify an entire rental period may be necessary. Let S(x) represent the cost of renting a saw for x days. Complete parts (a) through (m) below.

(c) Find S(1 1/10).
S(1 1/10)=60
(d) Find S(3 1/4).
S(3 1/4)=112
(e) Find S(5).
S(5)=138
(f) Find S(5 1/5).
s(5 1/5)=
Transcript text: A chain-saw rental firm charges $\$ 26$ per day or fraction of a day to rent a saw,plus a fixed fee of $\$ 8$ for re-sharpening the blade.Additional portions of a day are considered to a be a full day's rental,so rounding upward to identify an entire rental period may be necessary.Let $\mathrm{S}(\mathrm{x})$ represent the cost of renting a saw for x days.Complete parts(a)through(m) below. (c)Find $S\left(1 \frac{1}{10}\right)$ . \[ \mathrm{S}\left(1 \frac{1}{10}\right)=\$ 60 \] (d)Find $\mathrm{S}\left(3 \frac{1}{4}\right)$ . \[ S\left(3 \frac{1}{4}\right)=\$ 112 \] (e)Find $\mathrm{S}(5)$ . \[ S(5)=\$ 138 \] (f)Find $S\left(5 \frac{1}{5}\right)$ . \[ s\left(5 \frac{1}{5}\right)=\$ \]
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Solution

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Find \(S\left(5 \frac{1}{5}\right)\).

Calculate the number of days to be charged.

Since additional portions of a day are considered a full day's rental, we round \(5 \frac{1}{5}\) up to 6.

Calculate the rental cost.

The cost of renting a saw for x days is given by \(S(x) = 26x + 8\). In this case, \(x = 6\), so the cost is \(S(6) = 26(6) + 8 = 156 + 8 = 164\).

\(\boxed{164}\)

\(S\left(5 \frac{1}{5}\right) = 164\)

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