Question

solve equations with rational numbers
listen
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.
how many cookies did he bake on the second day?
enter your answer as a number, like this: 42

Explanation:

Step1: Define variable for day 1

Let $x$ = cookies baked on day 1.

Step2: Write day 2 and 3 amounts

Day 2: $2x$, Day 3: $\frac{1}{2}x$

Step3: Set up total equation

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

Step4: Combine like terms

$$\frac{2x + 4x + x}{2} = 224 \implies \frac{7x}{2} = 224$$

Step5: Solve for $x$

$$x = 224 \times \frac{2}{7} = 64$$

Step6: Calculate day 2 cookies

$$2x = 2 \times 64 = 128$$

Answer:

128