The product of two numbers is 1,360. The difference of the two numbers is 6. What are the two numbers?

2 Answers
Jun 5, 2018

40 and 34
OR
-34 and -40

Explanation:

Given that :
1) The product of two numbers is 1,360.

2) The difference of the two numbers is 6.

If the 2 numbers are x, and y

1) => x xx y =1360

=> x = 1360/y

and 2) => x-y =6

=> x= 6+y ---------(i)

Substituting value of x in 1),

=> (6+ y) y = 1360

=> 6y + y^2 -1360 =0

=> y^2 +6y -1360 =0

=> y^2 +40y -34y -1360 =0

=> y(y +40) - 34(y+40) = 0

=> (y-34)(y+40) =0

=> y=34 or y= -40

Taking y=34, and finding value of x from equation (2):

x-y =6
=> x - 34 = 6

=> x= 40

So, x= 40 and y =34

or

If we take y= -40, then

2) => x- (-40) =6

=> x= 6 - 40 = -34

So, x= -40, and y= -34

Answer: The two numbers are : 40 and 34
OR
-34 and -40

Jun 5, 2018

The numbers are 34 and 40

34 xx 40 = 1360 and 40-34=6

Explanation:

Factors of a number are always in pairs. If you write them in ascending order there are several things we can observe.
For example: the factors of 36.

1," "2," "3," "4," "6," "9," "12," "18," "36
color(white)(xxxxxxxxx.xxx)uarr
color(white)(xxxxxxxx.xxx)sqrt36

The outer pair, 1 and 36 have a sum of 37 and a difference of 35, whereas the innermost pair, 6 and 6 have a sum of 12 and a difference of 0

The factor in the middle is sqrt36. The further we are from the middle pair of factors, the greater is the sum and difference.

In this case, the factors of 1360 only differ by 6, which means that they are very close to its square root.

sqrt1360 = 36.878...

Explore numbers on either side of this. (Not more than 3 or 4 on either side.) You are also looking for factors which multiply to give a 0 at the end.

1360 div35 = 38.857
1360 div 40 = 34" "larr here we have them!