Expert: Josh - 4/6/2009

Question
Two consecutive numbers is 14 less than 10 times the smaller number (smaller
numbers equals X) find the number.

Answer
Hi Keith,

We can do this step by step using the information given.

By the way, i think something is missing...do you mean "the product of" two consecutive numbers is 14 less than 10 times the smaller number?

If the smaller of two consecutive numbers is X, then, the larger of the two number must be X+1.

So, the product of the two numbers is X(X+1) or X^2+X.

Translating the second part:
 If this is 14 less than 10*X, we have X^2+X=10X-14.

Rearranging the equation (add -10X+14 to both sides), we get a quadratic equation X^2-9X+14=0.

Observe that 2,7 are both factors of 14.
We factorize X^2-9X+14 as (X-2)(X-7).
(X-2)(X-7)=0, when X=2 or 7.

Check both solutions:

If X=2 and X+1=3, their product 2*3=6.
10*2=20. Clearly, 20-6=14 as claimed.

For X=7, X+1=8, their product 7*8=56.
10*7=70. Again, 70-56=14 as required.