Question

Priyanshi has 5 chocolates less than Dhruv. If both have 15 chocolates, find the number of chocolates each has?
(a) Priyanshi 5 chocolates, Dhruv 10 chocolates.
(b) Priyanshi 5 chocolates, Dhruv 1 chocolates.
(c) Priyanshi 3 chocolates, Dhruv 10 chocolates.
(d) Priyanshi 5 chocolates, Dhruv 2 chocolates.

Answer 1

Hint: Assume that Priyanshi has ‘$x$’ number of chocolates with her and Dhruv has ‘$y$’ number of chocolates with him. Form two linear equations, each having two variables, with the information provided. Solve these linear equations to find the number of chocolates they have.

Complete step-by-step answer:

A linear equation is an equation that describes a straight line on a graph. The word ‘linear’ means the degree or power of the variable must be 1. The standard form of a linear equation is $Ax+By=C$, where $A$, $B$ and $C$ are constants and $x$ and $y$ are variables. One can see that power of $x$ and $y$is unity or 1.

Now, let us come to the question.

Assume that Priyanshi has ‘$x$’ number of chocolates and Dhruv has ‘$y$’ number of chocolates. In the first condition it is given that Priyanshi has 5 chocolates less than Dhruv. Therefore, mathematically,

$x=y-5......................(i)$

In the second condition it is said that both have 15 chocolates. Therefore, mathematically,
$x+y=15...................(ii)$

So, now we have two equations in two variables. Let us solve these equations.

Substituting the value of $x$ from equation (i) in equation (ii), we get,
$\begin{align}
  & y-5+y=15 \\
 & 2y=20 \\
 & y=10 \\
\end{align}$

Now, substituting the value of $y$ in equation (i), we get,
$\begin{align}
  & x=10-5 \\
 & \text{ }=5 \\
\end{align}$

Therefore, Priyanshi has 5 chocolates and Dhruv has 10 chocolates.

Hence, option (a) is the correct answer.

Note: One can also solve the questions according to the options given. We can set the values of $x\text{ and }y$ according to the given options and check whether they satisfy the given conditions or not. The option which satisfies the conditions will be the correct answer. In option (a) we can see that Priyanshi has 5 chocolates and Dhruv has 10 chocolates. Here, Priyanshi has 5 chocolates less than Dhruv and they together have 15 chocolates. So, this option satisfies all the conditions and hence, it is the correct option.