Question

A rabbit on a controlled diet is fed a total of 1 kg of carrot every day. There are 2 types of carrots that are fed to the rabbit. Type X carrot contains \(60\%\) protein and type Y carrot contains \(80\%\) protein. If the rabbit must be fed 650 grams of protein everyday, then how many grams of type X carrot must be fed to the rabbit?

• A. 650 grams
• B. 750 grams
• C. 850 grams
• D. 950 grams

Answer 1

The Correct Option is B

Step 1: Define the Variables 

Let x be the amount (in grams) of type X carrot fed. Since the total amount of carrot fed is 1000 grams, the amount of type Y carrot fed is:

\[ 1000 - x \]

Step 2: Formulate the Protein Equation

The protein contribution from type X carrot is 0.6x, and from type Y carrot is 0.8(1000 - x). The total protein intake is given as 650 grams:

\[ 0.6x + 0.8(1000 - x) = 650 \]

Step 3: Solve for x

Expanding the equation:

\[ 0.6x + 800 - 0.8x = 650 \]

Combining like terms:

\[ -0.2x + 800 = 650 \]

Subtracting 800 from both sides:

\[ -0.2x = -150 \]

Dividing by -0.2:

\[ x = 750 \]

Final Conclusion:

The amount of type X carrot to be fed is 750 grams.