Question

The number of states that joined the United States between $1776$ and $1849$ is twice the number of states that joined between $1850$ and $1900.$ If $30$ states joined the United states between $1776$ and $1849$ and $x$ states joined between $1850$ and $1900,$ which of the following is true?
$\left( a \right)\,30x=2$
$\left( b \right)\,2x=30$
$\left( c \right)\,\dfrac{x}{2}=30$
$\left( d \right)\,x+30=2$

Answer 1

Hint: We know that the word twice means that two times which stands for multiple of two. So, if we say that a number $x$ is twice a number $y,$ then we can express this phrase Mathematically as $x=2y.$

Complete step by step solution:
Let us consider the given problem.
We are given that the number of states that joined the United States between $1776$ and $1849$ is $30.$
We are also given that the number of states that joined the United States between $1850$ and $1900$ is $x.$
We need to find the value of $x$ in order to find which of the given relations is true.
Now, let us consider the question. As we can see, it is given that the number of states that joined the United States between $1776$ and $1849$ is ‘twice’ the number of states that joined between $1850$ and $1900.$
So, we can say that the number of states that joined the United States between $1776$ and $1849$ is a multiple of $2$ and the number of states that joined the United States between $1850$ and $1900.$
Now, we can say that if $y$ is the number of states that joined between $1776$ and $1849,$ then $y=2x$ where $x$ is the number of states that joined between $1850$ and $1900.$
So, we will get $x=\dfrac{y}{2}.$
Here, we know that $y=30.$
So, we will get $x=\dfrac{30}{2}=15.$
We also know that $2\times 15=30.$
So, when we replace $15$ with $x,$ we will get $2x=30.$

Hence the required relation is $2x=30.$

Note:
We should always remember that twice a number $x$ implies that $2x.$ We also know that half a number $x$ implies that $\dfrac{x}{2}.$ Remember that $2$ more than a number $x$ implies that $2+x$ and $2$ less than a number $x$ implies that $x-2.$