The phrase “in terms of” signals that you need a formula for one amount while the other amounts remain letters. Write a linear equation by multiplying each per-gram rate by its number of grams and adding the contributions to the stated total. Then isolate the requested letter. Adding the other contributions instead of subtracting them would make the total too large.
Hints
- Hint 1
A unit rate such as food calories per gram turns grams into calories by multiplication. Protein and carbohydrate have the same rate in the table. How can you group their contributions?
- Hint 2
The bar’s food calories are the sum of all three contributions, not the calories from fat alone. Use the food-calorie column throughout; kilojoules are a different unit.
- Hint 3
To isolate a variable means to leave it alone on one side of an equation. Once you have the calorie total, which operation on both sides will get you closer to leaving fat alone?
Step-by-step
Build the calorie total and isolate fat
Step 1Write the total in food calories
No Desmos needed. The target is a formula in letters, which you can get directly from the table’s rates. Multiply each nutrient’s grams by its food calories per gram to get its contribution to the total. Protein and carbohydrate each contribute calories per gram; fat contributes . Add those contributions to match the 180 food calories:
- Step 2
Leave only fat’s calories on the left
The target is , so remove the protein and carbohydrate contribution. Subtract from both sides:
The minus sign matters: those calories are already part of the total, not extra calories to add.
- Step 3
Convert fat’s calories to grams
Each gram of fat contributes food calories. Divide every term by to leave alone:
- Step 4
Simplify the formula
Simplify to :
This expresses the grams of fat in terms of the protein and carbohydrate grams. Choice B.