DWhat two numbers have a product of 234 and a sum of 31?
AExample Graph:
B
C
DExample Graph:
Practice makes perfect
We want to complete the given Diamond Problem. Let's consider the given diagram and the pattern used in the problem!
We can fill the remaining corners when we find two rational numbers that sum up to 1.2 and have a product of 0.32.
Product (xy)
Sum (x+y)
Is the Sum Equal to 1.2?
0.32=0.16(2)
0.16+2=2.16
*
0.32=0.2(1.6)
0.2+1.6=1.8
*
0.32=0.32(1)
0.32+1=1.32
*
0.32=0.4(0.8)
0.4+0.8= 1.2
✓
Notice that we can complete our pattern when one factor is equal to 0.4 and the other is equal to 0.8. Let's complete our Diamond Problem!
Remember that this is one of the possible solutions. The Diamond Problem with x=0.8 and y=0.4 also corresponds to the pattern.
We want to complete the given Diamond Problem. Let's look at the diagram!
Notice that we know that x is 11. We can fill the remaining corners when we find a number corresponding to an arbitrary variable y such that the sum (x+y) is 25.
Let's consider the given Diamond Problem and the pattern used in the problem!
Notice that we know that x is - 9 and y is - 7. We can fill the remaining corners when we calculate the product and the sum of the factors.
x=- 9, y=- 7
Product (xy)
- 9( - 7)=63
Sum (x+y)
- 9+( - 7)=- 16
Now we can complete our Diamond Problem.
We want to complete the given Diamond Problem. Let's consider the given diagram and the pattern used in the problem!
We can fill the remaining corners when we find two rational numbers that sum up to 31 and have a product of 234.
Product (xy)
Sum (x+y)
Is the Sum Equal to 31?
234=2(117)
2+117=119
*
234=3(78)
3+78=81
*
234=6(39)
6+39=45
*
234=9(26)
9+26=35
*
234=13(18)
13+18= 31
✓
Notice that when the factors are equal to 13 and 18, the product is 234 and the sum is 31. In this case, one of the variables is equal to 13. The remaining variable is equal to 18. We can use this information to fill our Diamond Problem.
Remember that this is one of the possible solutions. The Diamond Problem for x=18 and y=13 also corresponds to the pattern.
