Question

Two factors of –48 have a difference of 19. The factor with a greater absolute value is positive.What is the sum of the factors?

Answer 1

48=2*24
=4*12
=3*16
=6*8
ab=-48
a-b=19
-16*3=-48
|-16-3|=19
16 is greater
16-3=13
13 should be the answer since 3 is negative

Answer 2

The sum of the factors is 13.

Explanation:

The factor with a greater absolute value is positive. If |a|>|b|, then the two factors of -48 are a and b, where a is positive and b must be negative.

`a* b=-48`

`ab=-48` ... (1)

The difference of factors is 19.

`a-b=19`

`a=19+b` ... (2)

From (1) and (2), we get

`(19+b)b=-48`

`19b+b^2+48=0`

`(b+16)(b+3)=0`

`b=-16,-3`

If b=-16, then using equation (1) the value of a is 3. Here |b|>|a|, so this condition is not true.

If b=-3, then using equation (1) the value of a is 16. Here |a|>|b|, so this condition is true. Therefore the two factors of -48 are 16 and -3.

The sum of two factors of -48 is

`16+(-30)=16-3=13`

Therefore the sum of the factors is 13.