Question

writing and solving an equation to model a situation
leena consumes 400 calories at breakfast and 350 calories at lunch. she consumes \\(\frac{2}{3}\\) of her daily calories at dinner. if \\(x\\) represents the calories consumed at dinner, which statements describe the situation? check all that apply.
\\(\square\\) leena consumed 1,500 calories at dinner.
\\(\square\\) the equation \\(\frac{2}{3}(x + 400 + 350) = x\\) can be used to model the situation.
\\(\square\\) leena consumed 500 calories at dinner.
\\(\square\\) the equation \\(\frac{2}{3}(x) = x(400 + 300)\\) can be used to model the situation.
\\(\square\\) leena consumed 1,000 calories at dinner.
\\(\square\\) the equation \\(\frac{2}{3}x(400 + 300) = x\\) can be used to model the situation.

Explanation:

Step1: Define total daily calories

Let total daily calories = $x + 400 + 350$, where $x$ = dinner calories.

Step2: Set up correct equation

Dinner calories = $\frac{2}{3}$ of total daily calories:
$$\frac{2}{3}(x + 400 + 350) = x$$

Step3: Simplify and solve for $x$

First simplify the sum inside the parentheses:
$$\frac{2}{3}(x + 750) = x$$
Multiply both sides by 3 to eliminate denominator:
$$2(x + 750) = 3x$$
Expand left side:
$$2x + 1500 = 3x$$
Subtract $2x$ from both sides:
$$x = 1500$$

Answer:

• Leena consumed 1,500 calories at dinner.
• The equation $\frac{2}{3}(x + 400 + 350) = x$ can be used to model the situation.