leena consumes 400 calories at breakfast and 350 calories at lunch. she consumes $\frac{2}{3}$ of her daily…

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.\n□ leena consumed 1,500 calories at dinner.\n□ the equation $\frac{2}{3}(x + 400 + 350)=x$ can be used to model the situation.\n□ leena consumed 500 calories at dinner.\n□ the equation $\frac{2}{3}(x)=x(400 + 300)$ can be used to model the situation.\n□ leena consumed 1,000 calories at dinner.\n□ the equation $\frac{2}{3}x(400 + 300)=x$ can be used to model the 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.\n□ leena consumed 1,500 calories at dinner.\n□ the equation $\frac{2}{3}(x + 400 + 350)=x$ can be used to model the situation.\n□ leena consumed 500 calories at dinner.\n□ the equation $\frac{2}{3}(x)=x(400 + 300)$ can be used to model the situation.\n□ leena consumed 1,000 calories at dinner.\n□ the equation $\frac{2}{3}x(400 + 300)=x$ can be used to model the situation.

Answer

Explanation:

Step1: Let the total daily - calorie intake be $y$.

The calories consumed at breakfast is 400, at lunch is 350, and at dinner is $x$. So, $y=x + 400+350$. Also, we know that $x=\frac{2}{3}y$.

Step2: Substitute $y$ in the second equation.

Substitute $y=x + 400+350$ into $x=\frac{2}{3}y$, we get $x=\frac{2}{3}(x + 400+350)$.

Step3: Solve the equation $x=\frac{2}{3}(x + 750)$.

Expand the right - hand side: $x=\frac{2}{3}x+\frac{2}{3}\times750$. Then $x-\frac{2}{3}x = 500$. $\frac{1}{3}x=500$, so $x = 1500$.

Answer:

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