Problem Solving

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. 1104
b. 972
c. 672
d. 294
e. 192

again if someone can tell me how to hide the OA I'll post it within the post..

thanks!

Let x be the middle number

Largest = 3*x

Smallest = 3x - 23

Sum = 3x-23+x+3x = 40

7x = 63

x = 9

Largest = 27, Smallest = 4, Middle = 9

So, product of all three integers = 27*4*9 = 972 (B)

OA = B

let the no be x,y,z

z=3y
x=z-23=3y-23

x+y+z=40
--->3y-23+y+3y=40

y=9
z=27
x=4
x*y*z=4*9*27=972
B

I don't know why you all are making fuzz for just a simple problem...
@sars72 you were going correct with the algebric solution but you missed the thing out in last step... Its very simple follow the steps below..

For solving |x-4| = 4-x,
Just break it in three steps..
1st step : Let x-4 be a positive no. so x>=4 and |x-4| = x-4
thus |x-4|=4-x --> x-4=4-x --> x=4.
but x>=4 hence there is only one solution for this condition i.e. x=4 ------- (i)

2nd step : Let x-4 be a negative no. so x<4 and |x-4| = -(x-4)
thus |x-4| = 4-x --> -(x-4) = 4-x --> 4=4 which is always true under specified condition...
thus x<4 is always true.. ------------------------------------------(ii)

so from (i) & (ii) we get that the overall solution of the equation |x-4| = (4-x) is x<=4 .

so u can easily splve it algebrically ... u can also use plugging in method as above..

[/quote]

Hey, you have posted in a wrong topic by mistake.

money9111 wrote: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. 1104
b. 972
c. 672
d. 294
e. 192

An alternate approach is to GUESS AND CHECK.

Let S = the smallest integer, M = the middle integer, and L = the largest integer.

Case 1: S = 1, with the result that L = 1+23 = 24 and that M = 40-1-24 = 15
Since the value of L (24) is not 3 times the value of M (15), Case 1 is not viable.

Since the value of L must be 3 times the value of M, L must be a MULTIPLE OF 3.
Thus, the next greatest option for L is 27.

Case 2: L=27, with the result that S = 27-23 = 4 and that M = 40-27-4 = 9
Success!
The value of L (27) is 3 times the value of M (9).

Resulting product:
27*4*9 = 972.

The correct answer is B.