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Find Two Numbers Whose Sum is 27 and Product is 182
Here when you add two numbers, you will get ‘27’ and when you multiply the same numbers, you will get ‘182’. Let’s find the two numbers now.
Let one number be ‘x’ and another number be ‘y’.
Then, the sum of two numbers will be:
x + y = 27 ….. (1)
The product of two numbers will be:
xy = 182 ….. (2)
You can also write (1) like this:
y = 27 – x
Substitute (y = 27 – x) in (2), you will get:
x (27 – x) = 182
27x – x² = 182
27x – x² – 182 = 0
This can be written as:
x² – 27x + 182 = 0
x² – 14x – 13x +182 = 0
x (x-14) – 13 (x -14) = 0
(x – 14) (x – 13) = 0
The value of x can be either 14 or 13.
If x = 14, y = 27 – 14
Then, y = 13
If x = 13, y = 27 – 13
Then, y = 14
So, the two numbers are 14 and 13.
Let’s check the answer:
The sum of two numbers, 14 + 13 = 27
The product of two numbers, 14 x 13 = 182.
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Source: Math Hello Kitty
Categories: Math
