Question

The sum or two numbers is 37 and the difference of thier squares is 185, the difference of the two numbers is A. 4 B. 5 C. 3 D. 10

Answer 1

The two numbers are 16 and 21.

Explanation:

Let the two numbers be x and y.

"The sum or two numbers is 37" can be written as:

x + y = 37

"the difference of their squares is 185" can be written as:

x^2 - y^2 = 185

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Rearrange the first equation to isolate one of the variables (x or y). Let's isolate x:

x + y = 37

x = 37 - y

Now use this expression of x in the second equation:

x^2 - y^2 = 185

(37 - y)^2 - y^2 = 185

y^2 - 74y + 1369 - y^2 = 185

-74y + 1369 = 185

-74y = - 1184

y = 16

Since x + y = 37,

x + 16 = 37

x = 21

CHECK:

Is their sum 37?: 16 + 21 = 37 YES

Is the difference of their squares 185?:

21^2 = 441

16^2 = 256

Difference = 185 YES

The two numbers are 16 and 21