The product of two consecutive integers is 600. Find the integers.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Let the consecutive numbers be x and x + 1

As their product is 600

x(x + 1) = 600

=> x^2 + x - 600 = 0

=> x^2 + 25x - 24x - 600 = 0

=> x(x + 25) - 24(x + 25) = 0

=> (x - 24)(x + 25) = 0

=> x = 24 and x = -25

The consecutive numbers can be 24 and 25 or -24 and -25

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givingiswinning | Student, Grade 10 | (Level 1) Valedictorian

Posted on

x(x + 1) = 600

x^2 + x = 600

x^2 + x - 600

x^2 + 25x - 24x - 600

x(x + 25) -24 (x + 25)

(x - 24) ( x + 25)

x = 24  x= -25

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

x(x + 1) = 600

distribute the x

x^2 + x = 600

subtract 600

x^2 + x - 600

find factors of -600 that add up to 1

x^2 + 25x - 24x - 600

find the greatest common factors:

x(x + 25) -24 (x + 25)

(x - 24) ( x + 25)

x = 24  x= -25

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