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One number is 5 more than another. The difference between their squares is 65. What are the numbers?

1 Answer

4 votes

Answer:

Explanation:

Let x be the larger number.

Let y be the smaller number.

x - y = 5

x^2 - y^2 = 65 Factor the left.

(x - y)(x + y) = 65 Substitute the first equation into this equation.

5 *(x + y) = 65 Divide both sides by 5

x + y = 65/5

x + y = 13

Now list the two binomials one after the other.

x + y = 13

x - y = 5 Add

2x = 18 Divide by 2

2x/2 = 18/2

x = 9

x + y = 13 Substitute 9 for x

9 + y = 13 Subtract 9 from both sides.

y = 13 - 9

y = 4

Answer

  • x = 9
  • y = 4
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