Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Sign up to join this community
I'm in algebra and this problem was under the lesson Factoring to Solve Quadratic Equations. The problem is the following:
The product of two consecutive numbers is 14 less than 10 times the smaller number. Find each number.
I've come up with $x$ and $10x-14$. I know that there should be two variables, but that's all I could come up with as far as an expression goes. If anyone can give me a better expression or teach me how to solve this it'd be greatly appreciated. Thank you.
Consecutive integers are x and x+1.
Product is $x(x+1)$
Thus the equation to solve is $x(x+1)=10x-14$
Call the smaller number $x$. Then we have
$$x(x+1) +14 = 10x$$
$$x^2 -9x + 14 = 0$$
$$(x -7)(x-2) = 0$$
so the solutions are $x=7$ or $x=2$ and so the smaller number is either $2$ or $7$. The larger number will obviously be $3$ or $8$ respectively.
