Question

When Billy's asked how old he is, he replies, "In two years I will be twice as old as I was five years ago." How old is he?

Answer 1

Answer: 12

Step-by-step explanation:

Let's algebraically represent this situation. Say his current age is x. We can rephrase the sentence to say that in two years, his age is the same as twice his age 5 years ago.

The phrase "in two years" means when his age is 2 more than his current age, or x + 2.

The phrase "same as" represents equality. The expressions on both sides have the same value.

The phrase "twice his age 5 years ago" is his age minus 5, multiplied by 2. We can write this as 2*(x-5).

Now that we have "translated" the equation from words to numbers, let's put it all in one equation and solve:

$x+2=2(x-5)$

$x+2=2x-10$ [Distributive Property]

$x+2-2x-2=2x-10-2x-2$ [Adding -2x-2 to both sides]

$-x=-12$ [Combining like terms and simplifying]

$x=12$ [Multiplying both sides by -1 to remove the negative]

Hence, Billy's age is 12.

Answer 2

Answer:

12 years old

Step-by-step explanation:

Set up the following equation:

x + 2 = 2(x - 5) (distribute the 2)

x + 2 = 2x - 10 (subtract 2 from both sides)

x = 2x - 12 (subtract 2x from both sides)

-x = -12 (multiply both sides by negative 1)

x = 12

Brainliest, please :)