Question

one positive number is 2 more than twice another. their product is 60.

step 2 of 2 : find the numbers by solving the equation.

Explanation:

Translate the problem into algebraic equations

Using the Quadratic Word Problems knowledge point
Let the smaller positive number be \(x\).
The other positive number is \(2x + 2\).
Their product is given as:

$$ x(2x + 2) = 60 $$

Write the quadratic equation in standard form

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK0
$$

Solve the quadratic equation by factoring

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK1
$$

Determine the positive numbers

Using the Quadratic Word Problems knowledge point
Since the problem states the numbers must be positive:

$$
LATEXBLOCK2
$$

The two positive numbers are 5 and 12.

Answer:

One positive number is 2 more than twice another. Their product is 60. Find the numbers by solving the equation.

The numbers are <blank>5</blank> and <blank>12</blank>.