Hi Gary!
So, let's say that a reciprocal number is 1 divided by a number q. So, the reciprocal of q for example is [tex] \frac{1}{q} [/tex]
Now, it asks us to find also a consecutive even number.
A consecutive number is the number next to another one. Theorically this means the consecutive of q is q+1, since you add 1 to find the number next to q but.....it asks for an 'even' number and even numbers are for example 2,4,6,8 ecc., they add always 2.
So our consecutive even number would be q+2
Of course you find the reciprocal the 1 / q+2
So, let's set up the equation
[tex] \frac{1}{q} + \frac{1}{q+2} = \frac{7}{24} [/tex]
Let's solve the equation by first finding the common denominator
[tex] \frac{24(q+2)+24q}{24q(q+2)}= \frac{7q(q+2)}{24q(q+2)} [/tex]
24q ≠ 0 -> q ≠ 0 and q+2 ≠ 0 -> q ≠ -2
24q + 48 + 24q = 7q^2 + 14q
-7q^2 - 14q + 24q + 24q + 48 = 0
-7q^2 + 34x + 48 = 0
7q^2 - 34x - 48 = 0
You can factor it.
(7x+8)(x-6) = 0
7x + 8 = 0 -> 7x = -8 -> x = -8/7
x - 6 = 0 -> x = 6
We choose the positive solution.
So one number is 6, then we find the even consecutive -> 6+2 = 8
Numbers are 6 and 8
Answer C
