If the difference of squares of two consecutive numbers is 93, then determine the smaller number. Ops: A. 48 B. 45 C. 46 D. 47
Question
If the difference of squares of two consecutive numbers is 93, then determine the smaller number.
Ops:
A. 48
B. 45
C. 46
D. 47
Solution
Let's denote the smaller number as x. Then the next consecutive number is x + 1.
According to the problem, the difference of the squares of these two numbers is 93. This can be written as:
(x + 1)^2 - x^2 = 93
Expanding and simplifying this equation gives:
x^2 + 2x + 1 - x^2 = 93 2x + 1 = 93 2x = 92 x = 46
So, the smaller number is 46. Therefore, the answer is C. 46.
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