Question

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

Answer 1

Answer:

Step-by-step 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