We will make use of the concept of prime factors for solving this question. The prime factors of 1517 are:
So, as can be clearly seen the Niagara Fall tour operator can either sell 37 tickets for $41 each or 41 tickets for $37 each.
Now, we know that we cannot reach $37 using just three bills. Thus, the only option left to us is $41 which can be broken down into three bills of $20,$20 and $1. This satisfies our condition.
Thus the cost of a ticket was $41 and 37 such tickets were sold.
The box should have base 52 cm by 52 cm and height 26 cm.
What is volume?
A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.
The Volume of a box with a square base x by x cm and height h cm is
Since the surface area directly affects the amount of material used, we can reduce the amount of material by reducing the surface area.
The surface area of the box described is
We need A as a function of x alone, so we'll use the fact that
⇒
So, the area becomes,
We want to minimize A, so
The second derivative test verifies that A has a minimum at this critical number:
which is positive at x = 52.
Now,
Hence, The box should have base 52 cm by 52 cm and height 26 cm.
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