SOLUTION: Find two numbers whose product is 48 and sum is 14? 2. Product -72 Sum -21

Question 124314: Find two numbers whose product is 48 and sum is 14?
2. Product -72 Sum -21
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

Let's list all of the factors of 48:

Factors of 48:
1,2,3,4,6,8,12,16,24,48

-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 48
1*48
2*24
3*16
4*12
6*8
(-1)*(-48)
(-2)*(-24)
(-3)*(-16)
(-4)*(-12)
(-6)*(-8)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 14

First Number	Second Number	Sum
1	48	1+48=49
2	24	2+24=26
3	16	3+16=19
4	12	4+12=16
6	8	6+8=14
-1	-48	-1+(-48)=-49
-2	-24	-2+(-24)=-26
-3	-16	-3+(-16)=-19
-4	-12	-4+(-12)=-16
-6	-8	-6+(-8)=-14

From this list we can see that 6 and 8 add up to 14 and multiply to 48

# 2

Let's list all of the factors of -72:

Factors of -72:
1,2,3,4,6,8,9,12,18,24,36,72

-1,-2,-3,-4,-6,-8,-9,-12,-18,-24,-36,-72 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -72
(1)*(-72)
(2)*(-36)
(3)*(-24)
(4)*(-18)
(6)*(-12)
(8)*(-9)
(-1)*(72)
(-2)*(36)
(-3)*(24)
(-4)*(18)
(-6)*(12)
(-8)*(9)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -21? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -21

First Number	Second Number	Sum
1	-72	1+(-72)=-71
2	-36	2+(-36)=-34
3	-24	3+(-24)=-21
4	-18	4+(-18)=-14
6	-12	6+(-12)=-6
8	-9	8+(-9)=-1
-1	72	-1+72=71
-2	36	-2+36=34
-3	24	-3+24=21
-4	18	-4+18=14
-6	12	-6+12=6
-8	9	-8+9=1

From this list we can see that 3 and -24 add up to -21 and multiply to -72

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