A hospital dietitian computes the daily calorie intake for a patient as 3000 calories. The calories allowed for lunch are twice the calories allowed for breakfast. The calories allowed for dinner are one and one-half the calories allowed for lunch. The allowance for an evening snack is 180 calories. How many calories are allowed for lunch?
Let "x" be the number of calories allowed for breakfast.
Lunch:2x
Dinner:1.5(2x)=3x
Total: x+2x+3x+180=3000
6x+180=3000
6x=2820
x=<<470=470>>470 calories. Answer: \boxed{470}.
Let's use algebra to solve this problem step by step.
Let X = calories allowed for breakfast
The calories allowed for lunch are twice the calories allowed for breakfast, so lunch = 2X
The calories allowed for dinner are one and one-half the calories allowed for lunch, so dinner = 1.5(2X)
The total daily calorie intake is 3000, so the equation is: X + 2X + 1.5(2X) + 180 = 3000
Simplifying the equation:
X + 2X + 3X + 180 = 3000
6X + 180 = 3000
Subtracting 180 from both sides:
6X = 2820
Dividing both sides by 6:
X = 470
Therefore, 470 calories are allowed for lunch.
To find the number of calories allowed for lunch, we need to follow the information given in the question.
Step 1: Let's assume the number of calories allowed for breakfast is x.
Step 2: According to the given information, the calories allowed for lunch are twice the calories allowed for breakfast. Therefore, the calories allowed for lunch would be 2x.
Step 3: The calories allowed for dinner are one and one-half times the calories allowed for lunch. Therefore, the calories allowed for dinner would be (1.5)*(2x) = 3x.
Step 4: We add up the calories allowed for each meal and snack to calculate the total daily calorie intake:
Breakfast: x calories
Lunch: 2x calories
Dinner: 3x calories
Evening Snack: 180 calories
Total daily calorie intake = x + 2x + 3x + 180 calories = 3000 calories
Step 5: Now, we can solve the equation to find the value of x:
6x + 180 = 3000
Subtract 180 from both sides:
6x = 2820
Divide both sides by 6:
x = 470
Therefore, the calories allowed for lunch would be 2x = 2 * 470 = 940 calories.