Question

Translate this problem to an equation and solve.
The product of 2 positive consecutive even integers is 48.
What is the smaller number?

Answer 1

you know the meaning of "consecutive" ?

Answer 2

Product means multiply.
Let the first even number be x and the consecutive even number be x + 2.

Answer 3

you know how to solve quadratic equations ?

Answer 4

no i dont know how to solve it

Answer 5

did u get the equation ?

Answer 6

no i dont get how to do it

Answer 7

Do you get how AnimEfReaK assigned the variables, (x) and (x+2)?

Answer 8

Further did you get how product indicates multiplication?

Answer 9

Which means x(x+2)=48 or x^2 + 2x = 48.

Answer 10

first integer = x
2nd integer = x + 2

x(x + 2) = 48 -- distribute
x^2 + 2x = 48
x^2 + 2x - 48 = 0

quadratic formula : (-b +- sq r b^2 - 4ac) 2a
a = 1, b = 2, and c = -48
now we sub

(-2 +- sq r 2^2 - 4(1)(-48)) / 2(1)
(-2 +- sq r 4 + 192) / 2
(-2 +- sq r 196)/2
(-2 +- 14)/2

(-2 + 14) /2 = 12/2 = 6
(-2 - 14)/2 = -16/2 = -8

smaller number is -8

Answer 11

\[x ^{2}+2x -48=0\]This factors nicely which is a method of solving a quadratic.
(x-6)(x+8) are the factors. Only one results in a positive integer
x-6 = 0
x=6
x+2 = 8