Question

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. What is the product of the three integers?A) 1,104B) 972C) 672D) 294E) 192

Answer 1

the answer is B

Explanation:

Answer 2

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

`a+b+c=40~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\a=3b\\\\\Rightarrow b=(a)/(3)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\a=c+23\\\\\Rightarrow c=a-23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Substituting the values of b and c from equations (ii) and (iii) in equation (i), we get

`a+(a)/(3)+a-23=40\\\\\\\Rightarrow (7a)/(3)=63\\\\\\\Rightarrow a=(63*3)/(7)\\\\\Rightarrow a=27.`

From equations (ii) and (iii), we get

`b=(27)/(3)=9`

and

`c=27-23=4.`

Therefore, we get

`abc=27*9*4=972.`

Thus, the required product of the three integers is 972.

Option (B) is CORRECT.