Question

hans spent three days baking 224 cookies. on the second day, he baked twice as many as he did on the first day. on the third day, he baked half as many as he did on the first day.
which equation represents the situation, if $x$ is the number of cookies hans baked the first day?
$2x + \frac{1}{2}x = 224$
$x + 2 + \frac{1}{2} = 224$
$224x + 2x + \frac{1}{2}x = 224$
$x + 2x + \frac{1}{2}x = 224$

Explanation:

Step1: Define daily cookie counts

Let $x$ = cookies baked on Day 1.
Day 2: $2x$ (twice Day 1)
Day 3: $\frac{1}{2}x$ (half Day 1)

Step2: Sum counts to total

Total cookies = Day1 + Day2 + Day3
$x + 2x + \frac{1}{2}x = 224$

Step3: Match to options

The derived equation matches the last option.

Answer:

$\boldsymbol{x + 2x + \frac{1}{2}x = 224}$