Call the numbers x and y. According to the first sentence, x + y = 67. According to the second sentence, x = y + 5. You can combine these two equations to find the values of these variables:
x + y = 67
(y + 5) + y= 67
2y = 62
y = 31
You can use this to find x by plugging in y to either original equation:
x = y + 5
x = 31 + 5
x = 36
A is the answer because it is the widest variety
First get all the terms on the same side:

Now solve using the quadratic formula which is:

Plug in the values:

So the answer is: