SOLUTION: In the following sum the same two numbers are needed. When they are added or mutliplied together, they form the answers for (a) and (b). I need to work out what theose numbers are

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Question 637069: In the following sum the same two numbers are needed. When they are added or mutliplied together, they form the answers for (a) and (b). I need to work out what theose numbers are

(a) ............+........... = 2.7
(b) ............x........... = 1.8


Can anone help me with the following I just cnat seem to get it thanks

I have already submitted this question but my email address was wrong
Found 2 solutions by ewatrrr, Maths68:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

The 'clue' to the problem is the numbers must end with something that

results in a zero in the hundredths place when multiplied: 

x + y = 2.7

x+%2B+%281.8%2Fx%29+=+2.7

 x^2 - 2.7x + 1.8 = 0   |

x+=+%282.7+%2B-+.3%29%2F%282%29+ 

 x =  1.5  0r  x = 1.2

Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Let x and y be the two numbers
x+y=2.7
x+y=27/10
10(x+y)=27
10x+10y=27.............(1)

xy=1.8
xy=18/10
x=18/10y...............(2)

Put the value of x from (2) to (1)
10(18/10y)+10y=27
18/y+10y=27
(18+10Y^2)/y=27
18+10Y^2=27y
10y^2-27y+18=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 10x%5E2%2B-27x%2B18+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-27%29%5E2-4%2A10%2A18=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+9+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+9+%29%29%2F2%5C10+=+1.5
x%5B2%5D+=+%28-%28-27%29-sqrt%28+9+%29%29%2F2%5C10+=+1.2

Quadratic expression 10x%5E2%2B-27x%2B18 can be factored:
10x%5E2%2B-27x%2B18+=+10%28x-1.5%29%2A%28x-1.2%29
Again, the answer is: 1.5, 1.2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B-27%2Ax%2B18+%29

So
y=1.5 or 1.2

Put the values of y in (1)
10x+10y=27.............(1)
Put y=1.5
10x+10(1.5)=27
10x+15=27
10x=27-15
10x=12
x=12/10
x=1.2

Put the values of y in (1)
10x+10y=27.............(1)
Put y=1.2
10x+10(1.2)=27
10x+12=27
10x=27-12
10x=15
x=15/10
x=1.5
So numbers are 1.2 and 1.5


Check
=====
xy=1.8
(1.2)(1.5)=1.8
1.8=1.8

x+y=2.7
1.2+1.5=2.7
2.7=2.7