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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