Question

A toll road charges trucks a toll for $\$3$ per axle. How do you write an expression for the total toll for a truck?

Answer 1

Hint: We are given that toll road charge a toll of $\$3$ per axle, we are asked to find the expression for the total toll for a truck, to answer this problem, we will first learn about the unitary method, we will work on example related to unitary method then we will learn how many axle can truck have, we consider it as ‘x’ and solve for the expression.

Complete step-by-step solution:
We are given that a toll road charges a truck a toll for $\$3$ per axle, we are asked to find an expression for the total toll of a truck.
To answer this problem, we first need to learn about unitary methods.
Unitary method is a technique that will help us in connecting the cost of an item per unit to any number of quantities.
Also it work in opposite way –
This method helps us in finding the cost of any number of items if we know what the cost of a single item is.
For example if we know that the cost of a pencil is one pen in $\$0.5$ then we have to look for the cost of 100 such pens.
So, since the cost of 1 pen $=\$0.5$ .
So, for cost of 100 pen, we multiply our cost as 1 pen by 100, hence cos of 100 pen –
$\begin{align}
  & =100\times \$0.5\\&=50\\\end{align}$
So, 100 such pens will cost $\$50$ .
Now let us work on our problem.
We have given that the cost toll for one axle is $\$3$ .
And we have to find the cost of the total toll for the truck.
We first see that different trucks have different numbers of axles. So, we consider that the truck has an ‘x’ number of axles.
Now, toll on 1 axle $=\$3$ .
S0, for toll on ‘x’ axle we multiply our equation by ‘x’. so we get –
Total toll on ‘x’ axle $=3\times x$
$=\$3x$ .


Note: We need to remember that the number of axles change per truck so here we took an arbitrary number ‘x’ to get our equation/expression.
Also if we have that cost of 10 item is 50 rupees than unitary method also help us to get cost of single unit as –
$10\text{ unit }=50\text{ rs}$ .
So, dividing both sides by 10, we get –
$\dfrac{10\text{unit}}{10}=\dfrac{50}{10}rs$
$\Rightarrow 1\text{ unit }=5Rs$
So, the cost of a single unit is rupees 5.
We need to be careful with dimension while solving such problems.