Question

The difference between two whole numbers is 26 and one number is three times the other. Find the numbers.
(a) 39 and 13
(b) 36 and 12
(c) 54 and 18
(d) 45 and 15

Answer 1

Hint: First express the word problem in the form of two variables (say x and y). Here, x would represent one number and y would represent the other number. Form another equation in x and y using the 2nd condition given.

Complete step by step solution:
For solving this question, we first try to convert the word problem into algebraic equations. Thus, according to the first condition, the difference between two whole numbers is 26. Let the larger number be x and the smaller be y. We have,
x – y = 26 -- (1)
Now, from the second condition, we have that one number is three times the other. Since, x is the larger number, we have,
x = 3y -- (2)
Substituting the value of (2) in (1), we have,
3y – y = 26
2y = 26
y = 13
Since, x = 3y, we have,
x = 39
Hence, the correct answer is (a) 39 and 13.

Note: In most of the algebraic problems, it is important to convert the problem in English into mathematical equations. Once, that is done, one can solve it manually or use matrix algebra to solve the problem. Generally, for an equation with 2 variables and 2 unknowns, we solve manually, while for a higher number of variables, we generally use matrix algebra.