A two-variable linear equation fits a mix with a fixed calorie total. Multiply each nut’s calories per ounce by its ounces, then add the contributions. Use Desmos to find how many calories remain after an ingredient with a fixed amount is included. The tempting mistake is to use that ingredient’s calories as the amount remaining.
Hints
- Hint 1
A unit rate tells you the calories in one ounce. Match each variable to its nut before multiplying: counts almond ounces, while counts peanut ounces. Which table row belongs with each letter?
- Hint 2
The cashew amount is already known, so it doesn’t need a variable. Multiply its calories per ounce by , then subtract that contribution from the planned total. What must the almonds and peanuts supply?
Step-by-step
Build the calorie total
Step 1Write the total-calorie equation
Multiply each calorie-per-ounce rate by its own ounces. The table gives calories from almonds and from peanuts. The ounces of cashews contribute calories. All three contributions make the planned total, so . Walnuts aren’t included in this mix.
- Step 2
Find the cashew calories
The cashew amount is fixed at ounces. Type in Desmos; it shows calories. Don’t attach to : counts almonds, not cashews.
- Step 3
Find what the other nuts must supply
Subtract the cashew calories from the planned total. Type on the next Desmos line; it shows . That’s the calories left for almonds and peanuts together, not the calories from cashews.
- Step 4
Relate the almond and peanut ounces
The almond and peanut terms from the total equation must equal the calories left: . This relates the ounces of almonds and peanuts in the finished mix. Choice B.