Question

a rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food x and food y. food x contains 10% protein and food y contains 15% protein. if the rabbits diet provides exactly 38 grams of protein daily, how many grams of food x are in the mixture.

a. 100
b. 140
c. 150
d. 160
e. 200

Explanation:

🆕 New Concept Discovered: Systems of Linear Equations
Using two equations to find two unknown values.

Step 1: Define the variables

Let \( x \) be the number of grams of food X in the mixture.
Let \( y \) be the number of grams of food Y in the mixture.

Step 2: Set up the system of equations

We are given two key pieces of information to build our equations:

1. Total mass of the mixture: The total daily amount of food is \( 300 \) grams.

$$ x + y = 300 $$

1. Total mass of protein: Food X contains \( 10\% \) protein, food Y contains \( 15\% \) protein, and the total protein is exactly \( 38 \) grams.

$$ 0.10x + 0.15y = 38 $$

Step 3: Solve the system of equations

We can express \( y \) in terms of \( x \) using the first equation:

$$ y = 300 - x $$

Now, substitute this expression for \( y \) into the second equation:

$$ 0.10x + 0.15(300 - x) = 38 $$

Distribute the \( 0.15 \):

$$ 0.10x + 45 - 0.15x = 38 $$

Combine the \( x \) terms:

$$ -0.05x + 45 = 38 $$

Subtract \( 45 \) from both sides:

$$ -0.05x = -7 $$

Divide by \( -0.05 \):

$$ x = \frac{-7}{-0.05} = 140 $$

Answer:

B. 140