SOLUTION: The product of two consecutive numbers is 14 less than 10 times the smaller number. Find each number.

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Question 188235This question is from textbook Algebra 1
: The product of two consecutive numbers is 14 less than 10 times the smaller number. Find each number. This question is from textbook Algebra 1

Answer by solver91311(24713) About Me  (Show Source):
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Your question doesn't make much sense unless you specify that the numbers are integers, whole numbers, natural numbers, or counting numbers, because 'consecutive' doesn't have any meaning unless you are dealing with these sorts of numbers.

Presuming that you meant to say: "The product of two consecutive integers is 14 less than 10 times the smaller integer. Find each integer," proceed thus:

Let the first integer be x. Then the next consecutive integer must be x + 1.

The product of the two integers is then:



Ten times the smaller integer is 10x. And 14 less than that is 10x - 14, so:



Put the quadratic into standard form:



Since -7 + (-2) = -9 and (-7)(-2) = 14, this factors:



Hence,



or



So your numbers are either 2 and 3 or 7 and 8.

Check:





You can do the arithmetic to check both sets of answers.

John