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Answer: The Van needs 18 gallons of gas to travel 360 miles.
Step-by-step explanation: Given that a Van travels 300 miles on 15 gallons of gas.
We are to find the number of gallons that the Van needs to travel 360 miles.
We will be using the UNITARY method to solve the given problem.
Number of gallons needed to travel 300 miles = 15.
So, number of gallons needed to travel 1 mile will be
[tex]\dfrac{15}{300}=\dfrac{1}{20}.[/tex]
Therefore, the number of gallons needed to travel 360 miles is given by
[tex]\dfrac{1}{20}\times 360=18.[/tex]
Thus, the Van needs 18 gallons of gas to travel 360 miles.
Amount of gas required to travel [tex]360\text{ miles}[/tex] is [tex]\boxed{\bf 18\text{\bf\ gallons}}[/tex].
Further explanation:
The word problems can be solved from the unitary method.
The unitary method is a method in which we have to first find the value of a single unit then further find the required value by multiplying the single unit value.
Given:
A van travelled [tex]300\text{ miles}[/tex] on [tex]15\text{ gallon}[/tex] of gas.
Calculation:
Step 1:
First we have to find the number of gallons in one mile.
It is given that the number of gallons needed to travel [tex]300\text{ miles}[/tex] is equal to [tex]15\text{ gallon}[/tex].
Use the unitary method to calculate the number of gallons in one mile.
It is calculated as follows:
[tex]\begin{aligned}\text{Number of gallon}&=\dfrac{15}{300}\\&=\dfrac{1}{20}\end{aligned}[/tex]
Step 2:
Now, we have to calculate the number of gallons needed to travel in [tex]360\text{ miles}[/tex].
Use the unitary method to calculate the required value by multiplying the single unit value.
The number of gallons in one mile is [tex]\frac{1}{20}[/tex].
Therefore, the number of gallons in [tex]360\text{ miles}[/tex] is calculated as follow:
[tex]\begin{aligned}\text{Number of gallon}&=\dfrac{1}{20}\cdot 360\\&=18\end{aligned}[/tex]
Thus, the Van requires [tex]\boxed{\bf 18\text{\bf\ gallons}}[/tex] of gas to travel [tex]360\text{ miles}[/tex].
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Answer details:
Grade: Junior school
Subject: Mathematics
Topic: Unitary method
Keywords: Van, gallons of gases, miles, travels, number of gallons, unitary method, multiply, single unit, linear equation, distance, equation.
