Question

Product of two numbers is 18.75. if one number is three times the other, then find a larger number.

Answer 1

Hint: For solving our problem, we formulate one equation by using the product statement and another equation by using the fact that one number is three times other and thus evaluate the required part of the statement.

Complete step-by-step answer:
We are given that the product of two numbers is 18.75. Another equation which is given is one number is three times the other number. By using both of the equations we can easily find out the respective numbers.
Now, we assume the first number to be x. From the second part of the statement, the second number would be 3x. Also, from the first statement the product of x and 3x is 18.75. Hence, it can be mathematically expressed as:
$\begin{align}
  & x\times 3x=18.75 \\
 & 3{{x}^{2}}=18.75 \\
 & {{x}^{2}}=\dfrac{18.75}{3} \\
 & {{x}^{2}}=6.25 \\
\end{align}$
Now, taking the square root of both the sides we get,
$\begin{align}
  & \sqrt{{{x}^{2}}}=\sqrt{6.25} \\
 & x=\pm 2.5 \\
\end{align}$
First, taking the positive value of x, we get a larger number as, $2.5\times 3=7.5$.
Now, taking the negative value of x, we get a larger number as, -2.5 because -7.5 is smaller than -2.5.
Therefore, the two possible solutions are 7.5 and -2.5.

Note: The key step for solving this problem is the knowledge of algebraic expression to a greater extent. We must manipulate the problem into some equation which is useful to get values for variables. Also, students must take care about both the values of x and provide the large number accordingly.