Question

An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.

Answer 1

Answer:

3, 12

Step-by-step explanation:

Et x and y be the required integers.

Case 1: x = 5y - 3...(1)

Case 2: xy = 36

Hence, (5y - 3)*y = 36

$5 {y}^{2} - 3y = 36 \\ 5 {y}^{2} - 3y - 36 = 0 \\ 5 {y}^{2} - 15y + 12y - 36 = 0 \\ 5y(y - 3) + 12(y - 3) = 0 \\ (y - 3)(5y + 12) = 0 \\ y - 3 = 0 \: or \: 5y + 12 = 0 \\ y = 3 \: \: or \: \: y = - \frac{12}{5} \\ \because \: y \in \: I \implies \: y \neq - \frac{12}{5} \\ \huge \purple{ \boxed{ \therefore \: y = 3}} \\ \because \: x = 5y - 3..(equation \: 1) \\ \therefore \: x = 5 \times 3 - 3 = 15 - 3 = 12 \\ \huge \red{ \boxed{ x = 12}}$

Hence, the required integers are 3 and 12.

Answer 2

Answer:

3 and 12

Step-by-step explanation:

Let's call the numbers x and 5x - 3. We can write:

x * (5x - 3) = 36

5x² - 3x = 36

5x² - 3x - 36 = 0

(5x + 12)(x - 3) = 0

x = -12/5 or x  =3

Since -12/5 is not an integer the answer must be x = 3 which makes the numbers 3 and 12.