Question

2 numbers that subtract to 20 and multiply to 125

Answer 1

Answer: 25 and 5

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That was from the game Prodigy. I had the same question then figured it out.  

Step by step explanation: 25 - 5 is 20

25 multiplied by 5 is 125.

Answer 2

SOLUTION

COMPLETE QUESTION

2 numbers that subtract to 20 and multiply to 125. Find the numbers

EVALUATION

Let the numbers are a and b

By the condition 1

a - b = 20 - - - - - - (1)

By the condition 2

ab = 125 - - - - - - - (2)

From Equation 1 we get

a = b + 20

From Equation 2 Putting the value of a we get

$\displaystyle \sf{ (b + 20)b = 125}$

$\displaystyle \sf{ \implies {b}^{2} + 20b - 125 = 0}$

$\displaystyle \sf{ \implies {b}^{2} + (25 - 5)b - 125 = 0}$

$\displaystyle \sf{ \implies {b}^{2} + 25b - 5b - 125 = 0}$

$\displaystyle \sf{ \implies b(b + 25) - 5(b + 25) = 0}$

$\displaystyle \sf{ \implies (b + 25) (b - 5) = 0}$

b + 25 = 0 gives b = - 25

b - 5 = 0 gives b = 5

When b = - 25 we have a = - 5

When b = 5 we have a = 25

Taking both numbers as positive

The numbers are 5 and 25

Hence the required numbers are 5 , 25

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