Find two consecutive whole numbers where the product of the larger and 10 more then the smaller is 90.

Answer 1

Hi Pedro, let x be the first and smaller of the two consecutive numbers. Then x + 1 will be the second and larger one.

Equation to solve:

The second number times 10 plus the smaller number equals 90

(x + 1) * (x + 10) = 90

x² + 11x + 10 = 90

Subtract 90 from both sides:

x² + 11x - 80 = 0

Factor:

(x-5) * (x - 16) = 0

Use the zero product rule:

x - 5 = 0

x = 5

And

x + 16 = 0

x = -16

Solution:

x is the smaller number and equals 5.

x + 1 is the larger number and equals 6.

Second solution:

x is the smaller number and equals -16

x + 1 is the larger number and equals -15

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