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Popular Word Problems >

A positive number is one-half another number. The sum of the numbers is 18 less than the square of the smaller number. What are the numbers?

Solution

A p os i t i v e n u mb er i s o n e - ha l f an o t h er n u mb er . T h e s u m o f t h e n u mb ers i s 18 l ess t han t h e s q u a re o f t h e s ma ll er n u mb er . Wha t a re t h e n u mb ers ?

Solution

The numbers : 6, 12

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x = \frac{1}{2} y

x + y = x^{2} - 18

Solve the system of equations:

x = \frac{1}{2} y, x + y = x^{2} - 18 : (x = 6, x = - 3, y = 12 y = - 6)

Select positive solutions:

12, 6

The numbers : 6, 12

Popular Examples

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