Question

Find two positive numbers whose difference is 3 and whoseproduct is 180. Write your answers from least to greatest with acomma separating each answer. For example: 4,9

Answer 1

12, 15

Explanation:

We use a system of equations to solve this question.

I am going to call the two numbers x and y.

Difference is 3

This means that: x - y = 3

Product is 180

This means that: xy = 180

Solving the system:

From the first equation: x = 3 + y

Replacing on the second equation:

(3+y)*y = 180

y²+3y = 180

y²+3y-180 = 0

Here we apply Bhaskara, with a = 1, b = 3, c = -180.

The solutions are y = -15 and y = 12.

The exercise asks only for positive numbers, so we use y = 12, which is one of the numbers.

The other number is: x = y+3 = 12+3 = 15

So the answer, in the format specified, is:

12, 15