Question

If $x = 3t,y = \dfrac{1}{2}\left( {t + 1} \right)$ then the value of t for which $x = 2y$ is
A) 1
B) $\dfrac{1}{2}$
C) -1
D) $\dfrac{2}{3}$

Answer 1

Hint:
We are given the values of x and y to be $x = 3t,y = \dfrac{1}{2}\left( {t + 1} \right)$ and we are also given a condition $x = 2y$ and to find the value of t we need to substitute the the given values in the condition to get the value of t.

Complete step by step solution:
We are given that $x = 3t,y = \dfrac{1}{2}\left( {t + 1} \right)$……..(1)
And we are given a condition $x = 2y$……….(2)
Now we are asked to find the value of t when it satisfies the above condition
So lets substitute the values of x and y in (2)
$
   \Rightarrow 3t = 2\left( {\dfrac{1}{2}\left( {t + 1} \right)} \right) \\
   \Rightarrow 3t = t + 1 \\
 $
Bringing all the terms to one side we get
$
   \Rightarrow 3t - t - 1 = 0 \\
   \Rightarrow 2t = 1 \\
   \Rightarrow t = \dfrac{1}{2} \\
 $
Hence we get the value of t to be $\dfrac{1}{2}$

Therefore the correct option is b.

Note:
1) In mathematics, a polynomial is a kind of mathematical expression. It is a sum of several mathematical terms called monomials. That is, a number, a variable, or a product of a number and several variables.
2) In algebra, when letters, numbers, and arithmetic symbols occur together, the understanding is that the letters stand for variables, which are either symbols of their own, numbers not yet known, or numbers that change during the course of the problem (such as time).
3) A polynomial is an algebraic expression in which the only arithmetic is addition, subtraction, multiplication and whole number exponentiation.
4) If harder operations are used, such as division or square roots, then this algebraic expression is not a polynomial. Polynomials are often easier to use than other algebraic expressions.