Question

The sum of three consecutive multiples of \[9\] is \[135\], then the multiples are
A) \[36,45,54\]
B) \[45,54,63\]
C) \[27,36,45\]
D) None of the above

Answer 1

Hint: Then find the multiples by algebra method. The meaning of a multiple in mathematics is the product result of one number multiplied by another number. Numbers which follow each other in order, without gaps, from smallest to largest. Examples are \[22,24,26,28\] and \[30\] are consecutive even numbers and \[40,45,50,55\] are consecutive multiples of \[5\].

Complete step by step solution:
Here first we assume the three consecutive multiples of \[9\]. Then adding those three is equal to \[135\].
Let \[9x\],\[9\left( {x + 1} \right)\],\[9\left( {x + 2} \right)\] be three consecutive multiples of \[9\].
Since, the sum of three consecutive multiples of \[9\] is \[135\].
Hence \[9x + 9\left( {x + 1} \right) + 9\left( {x + 2} \right) = 135\]---(1)
Simplify the equation (1), we get
\[27x + 27 = 135\]---(2)
Divided by \[27\]throughout the equation (2), we get
\[x + 1 = 5\]--(3)
Solving the equation (3), we get
\[x = 4\].
Put \[x = 4\] in the three consecutive multiples of \[9\] we get \[36,45,54\].
Hence, the three consecutive multiples of \[9\] whose sum \[135\] are \[36,45,54\]. So, Option (A) is correct.

Note:
Note that the arithmetic operations of addition, subtraction, multiplication, and division help us solve mathematical problems. Algebra deals with these concepts and can be considered as generalized arithmetic. An equation is a mathematical sentence with an equal sign.