Respuesta :
Answer: The correct option is (B) 972.
Step-by-step explanation: Given that the sum of three integers is 40. The largest integer is 3 times the middle integer, and the smallest integer is 23 less than the largest integer.
We are to find the product of the three integers.
Let a, b and c represents the three integers in descending order.
Then, according to the given information, we have
[tex]a+b+c=40~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\a=3b\\\\\Rightarrow b=\dfrac{a}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\a=c+23\\\\\Rightarrow c=a-23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the values of b and c from equations (ii) and (iii) in equation (i), we get
[tex]a+\dfrac{a}{3}+a-23=40\\\\\\\Rightarrow \dfrac{7a}{3}=63\\\\\\\Rightarrow a=\dfrac{63\times3}{7}\\\\\Rightarrow a=27.[/tex]
From equations (ii) and (iii), we get
[tex]b=\dfrac{27}{3}=9[/tex]
and
[tex]c=27-23=4.[/tex]
Therefore, we get
[tex]abc=27\times9\times4=972.[/tex]
Thus, the required product of the three integers is 972.
Option (B) is CORRECT.
