Question

How do you write a linear equation that relates the cost c and the number x of copies delivered if the cost to a newspaper company for Sunday home delivery is approximately \[\$ 0.45\] per newspaper with a fixed cost of \[\$ 2,080,000\] ?

Answer 1

Hint: Here we have a simple problem, First we need to convert the given word problem into an algebraic expression and then we simplify the equation to get the result. Here we need to find the equation of cost ‘c’.

Complete step by step solution:
Given,
Number ‘x’ of copies delivered and the cost to a newspaper company for Sunday home delivery is approximately \[\$ 0.45\] per newspaper.
We don’t know the number of copies delivered.
So we will have
  \[ \Rightarrow x \times \$ 0.45\] .
Also they mentioned a fixed cost of \[\$ 2,080,000\] . That is no matter how many copies delivered the cost \[\$ 2,080,000\] is fixed then we have,
 \[ \Rightarrow \$ 2,080,000 + \left( {x \times \$ 0.45} \right)\] . That is this is the required result.
That is the cost is given by
 \[ \Rightarrow c = \$ 2,080,000 + \left( {x \times \$ 0.45} \right)\] .
So, the correct answer is “$c = \$ 2,080,000 + \left( {x \times \$ 0.45} \right)$”.

Note: Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation \[( + )\] . Similarly If we have ‘less’ or ‘difference’ we use subtraction \[( - )\] . If we have a ‘quotient’ we use division operation \[( \div )\] . To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.
In the obtained answer ‘x’ is the unknown value or variable. If we know the value of ‘x’, that is the number of deliveries we can find the exact cost of the newspaper. Suppose let’s say 100 copies are delivered then all we need to do is substitute the ‘x’ as 100 then we will have the required answer.