Question

One integer is 3 more than 5 times another. The product is 54, what are the two integers?

Answer 1

Answer:

The two integers are 18 and 3.

Step-by-step explanation:

Consider the provided information.

It is given that One integer is 3 more than 5 times another.

Let us consider the integer is x.

Then 3 more than 5 times of x is:

$3+5x$

The product of the provided two numbers is 54. i.e.

$x(3+5x)=54$

$3x+5x^2=54$

$5x^2+3x-54=0$

Use the formula of the quadratic equation:

For the equation $ax^2+bx+c=0$ the solutions are:

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

By comparing the obtained equation with the above equation, it can be concluded that a = 5, b = 3 and c = -54. Substitute the these values in the above formula.

$x_{1,\:2}=\frac{-3\pm \sqrt{3^2-4\cdot \:5\left(-54\right)}}{2\cdot \:5}$

$x_{1,\:2}=\frac{-3\pm\sqrt{3^2+4\cdot \:5\cdot \:54}}{2\cdot \:5}$

$x_{1,\:2}=\frac{-3\pm\sqrt{1089}}{10}$

$x_{1,\:2}=\frac{-3\pm33}{10}$

$x_1=\frac{-3+33}{10}$ or $x_2=\frac{-3-33}{10}$

$x_1=\frac{30}{10}$ or $x_2=\frac{-36}{10}$

$x_1=3$ or $x_2=\frac{-18}{5}$

As we have given that numbers are integer, therefore ignore $x_2=\frac{-18}{5}$

Thus, the value of x is 3 or one number is 3.

Then 3 more than 5 times of x is: 3 + 5(3) = 18.

Therefore, the two integers are 18 and 3.