Leena consumes 400 cal at breakfast and 350 cal at lunch. She consumes 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. Lena consumed 1500 cal at dinner. Do you equation 2/3 (x+400+350)=x can be used to model the situation. Lena consumed 500 cal at dinner. Lena consumed 1000 cal at dinner. The equation 2/3(x)=x(400+350) can be used to model the situation. The equation 2/3x(400+350)=x Can’t be used to model the situation

1) Data:

Meal                calories consumed

Breakfast          400 cal
Lunch               350 cal
Dinner                x
                       ------------------
Total                 400 + 350 + x = 750 + x

2) Equation:

She consumes 2/3 of her daily calories at dinner => (2/3)[750+x] = x

3) Analyze each statement:

a) Lena consumed 1500 cal at dinner.

Solve the equation to find if the statement is true:

(2/3)[750+x] = x

2(750+x) = 3x

1500 + 2x = 3x

1500 = 3x - 2x

x = 1500

Conclusión: TRUE stament.

b) Do you equation 2/3 (x+400+350)=x can be used to model the situation.

That is the same equation that I found above.

Conclusion: TRUE statement

c) Lena consumed 500 cal at dinner.

She consumed (2/3) * 1500 = 500 cal

Conclusion: TRUE statement

d) Lena consumed 1000 cal at dinner.

No, we calculated that she consumed 500 cal at dinner.

Conclusion: FALSE statement

e) The equation 2/3(x)=x(400+350) can be used to model the situation.

No: (2/3) x = 500 and x(400+350) = 500*750 = 375,00, which are not equal.

Conclusion: FALSE statement.

f) The equation 2/3x(400+350)=x Can’t be used to model the situation

No: in that equation the variable x cancels out because it appears a factor at both sides.

Conclusion: TRUE statement