A price per kilogram is a unit rate: multiply it by kilograms to find that produce’s cost. Add the costs to match the total, then get the requested letter alone while keeping the other letters. Scaling every term can clear decimal prices before you rearrange. Watch that each price stays with its own produce, and divide by the coefficient of the letter you want.
Hints
- Hint 1
A price per kilogram is a unit rate. Multiplying it by kilograms gives dollars, so is the apple cost. What terms give the carrot and kale costs?
- Hint 2
All three prices are multiples of a quarter dollar. Multiply every term of the cost equation by , including the total, to remove the decimals. Which whole-number coefficient goes with each letter?
- Hint 3
The question wants alone, while and stay in the expression. Move the apple and carrot terms to the other side, then undo multiplication by kale’s coefficient.
Step-by-step
Write the total cost and isolate kale
Step 1Turn the prices into a cost equation
Each price is per kilogram, so multiply it by that produce’s kilograms. The apple cost is , the carrot cost is , and the kale cost is . They add up to the $100 total: .
- Step 2
Clear the decimal prices
Type in table order, then type and . Desmos shows and . Multiply every term, including the total, by to keep the equation balanced. So the cost equation becomes .
- Step 3
Leave the kale term on one side
Subtract the apple and carrot terms from both sides: .
- Step 4
Get kilograms of kale alone
Since multiplies , divide both sides by : . This gives kilograms of kale in terms of the apple and carrot kilograms. Choice D.