Question

Dave won a hot dog eating contest by eating 18 hot dogs in 10 minutes. He ate two more than twice the amount of the runner-up. Which equation, when solved for x, gives the number of hot dogs the runner-up ate? A) 2x − 2 = 18 B) 2x + 2 = 18 C) x 2 − 2 = 18 D) x 2 + 2 = 18

Answer 1

When solved for x, the runner-up ate 2x + 2 = 18

Explanation:

Dave won by eating 18 hot dogs

He ate two more than twice the amount of the runner-up.

Suppose the runner-up ate x-hot dogs.

That means Dave ate two more than twice of x. This can be written as

Twice of x is 2x

And two more than twice of x is 2x + 2.

So, Dave ate (2x + 2) hot dogs.

Since we already know that Dave ate 18, we can say

2x + 2 = 18

2x = 16

x = 8

Answer 2

The correct anser is option

B. 2x + 2 = 18

Explanation:

Let the number of hot dogs eaten by the runner up be represented by x

If Dave ate 2 more than twice x, this means that the number eaten by him = 2x + 2

Since the total number of hot dogs eaten by Dave is 18

Therefore, the equation will be

2x + 2 = 18

So the number of hot dogs eaten by the runner-up is determined by solving for x

2x= 18-2

2× = 16

x = 16/2

x = 8

The runner up are 8

While Dave are

2×8 + 2 = 18.