Question

The sum of two numbers is $ 25 $ and their difference is $ 13. $ find their product.
A. $ 104 $
B. $ 114 $
C. $ 315 $
D. $ 325 $

Answer 1

Hint: Understand the given data and find the correlation between the two. For two unknown terms, assume two variables as the reference value and frame the equations and simplify for the required resultant value.

Complete step-by-step answer:
Let us assume that the two unknown numbers be “x” and “y”
Given that: The sum of two number is $ 25 $
Convert the given statement in the form of the mathematical expression.
 $ x + y = 25 $ ….. (A)
Also, given that difference is $ 13. $
 $ x - y = 13 $ ….. (B)
Add equations (A) and (B),
 $ x + y + x - y = 25 + 13 $
Like terms with the same value and the opposite sign cancel each other.
 $ x + x = 38 $
Simplify the above expression –
 $ 2x = 38 $
Term multiplicative on one side if moved to the opposite side, then it goes to the denominator.
 $ x = \dfrac{{38}}{2} $
Find factors for the term on the numerator of the above expression-
 $ x = \dfrac{{19 \times 2}}{2} $
Common factors from the numerator and the denominator cancel each other.
 $ x = 19 $ …. (C)
Place the above value in expression (A)
 $ 19 + y = 25 $
Make the required term the subject, and move constant on the opposite side. When you move any term from one side to the opposite side then the sign of the terms also changes. Positive term becomes negative.
 $ y = 25 - 19 $
Simplify the above expression-
 $ y = 6 $ …. (D)
Now, the product of the terms $ = 19(6) $
Simplify finding the product –
Product $ = 114 $
From the given multiple choices – the option B is the correct answer.
So, the correct answer is “Option B”.

Note: Don’t get confused between the word statements. Always remember that the like terms with different signs and the same value cancel each other. Be good in finding the factors and remove common factors from the numerator and the denominator cancels each other.