Question

Two numbers differ by 10 and have a product of 704. Which of the following equations could be used to find the two numbers?

A. x(10 – x) = 704

B. x(10x) = 704

C. x(x – 10) = 704

D. x + (x – 10) = 704

Answer 1

can anybody explain?

Answer 2

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Answer 3

C would be the Answer I believe:

x(x – 10) = 704

(x-10) part gives it away since the two numbers differ by 10.

Solving for this you would see \[x(x-10) = 704\]
Simplifying becomes\[(x^2-10x) = 704\]Though to solve for that you have to use the method of completing the square. If you do that you find: \[x^{2}-10x+25 = 704\]
add 25 to both sides you find\[(x-5)^{2} = 729\] Square root both sides you get (x-5) = 27 or (x-5) = -27

Solve for x you find:
x = -22 or x = 32

If you plug those back into the original equation it gives 704.

Answer 4

Thank you so much!!!

Answer 5

No problem =)