Answer:
(a) 31.9 m
(b) W = 5.9n - 3.5
Step-by-step explanation:
Part (a)
In a warehouse there are two types of shelves, type R and type S.
These two types of shelves are arranged into shelving units that form a sequence of patterns.
For each arrangement of shelving units, the number of type S shelves is one less than the number of type R shelves.
The first three terms in the sequence are:
[tex]2R + S\\\\3R + 2S\\\\4R + 3S[/tex]
Therefore, if a shelving unit has 6 type R shelves, it will have 5 type S shelves:
[tex]6R + 5S[/tex]
Given that the width of a type R shelf is 2.4 m and the width of a type S shelf is 3.5 m, then the total width of a shelving unit that has 6 type R shelves is:
[tex]\textsf{Width}=6 \cdot 2.4 + 5 \cdot 3.5\\\\\textsf{Width}=14.4 + 17.5\\\\\textsf{Width}=31.9\; \sf m[/tex]
[tex]\dotfill[/tex]
Part (b)
As the number of type S shelves is one less than the number of type R shelves, and given that a shelving unit has 'n' type R shelves and the total width of this shelving unit is W meters, then:
[tex]W=nR + (n - 1)S[/tex]
Given that the width of type R shelf is 2.4 m and the width of type S shelf is 3.5 m, then the expression for W into terms of n is:
[tex]W=n(2.4) + (n - 1)(3.5)\\\\W=2.4n + 3.5n-3.5\\\\W=5.9n-3.5[/tex]
