Question

10
select the correct answer.
malik is baking pumpkin bread and banana bread for friends and family. his pumpkin bread recipe calls for 4 eggs and 3\frac{1}{2} cups of flour, and banana bread recipe calls for 1 egg and 1\frac{1}{2} cups of flour. malik has 14 eggs, 16 cups of flour, and plenty of other ingredients to make multiple loaves.
what is one combination of breads malik can bake without getting more ingredients?
a. 3 loaves of pumpkin bread and 3 loaves of banana bread
b. 1 loaf of pumpkin bread and 9 loaves of banana bread
c. 2 loaves of pumpkin bread and 6 loaves of banana bread
d. 5 loaves of pumpkin bread and 1 loaf of banana bread

Explanation:

Let \( x \) be the number of pumpkin bread loaves and \( y \) be the number of banana bread loaves.
The egg constraint: \( 4x + y \leq 14 \) (since pumpkin bread needs 4 eggs per loaf, banana needs 1).
The flour constraint: \( 3\frac{1}{2}x + 1\frac{1}{2}y \leq 16 \) (or \( \frac{7}{2}x+\frac{3}{2}y\leq16 \), multiply by 2: \( 7x + 3y \leq 32 \)).

Step 1: Test Option A (\( x = 3, y = 3 \))

• Eggs: \( 4(3)+3 = 15 \). But \( 15>14 \), violates egg constraint. Eliminate A.

Step 2: Test Option B (\( x = 1, y = 9 \))

• Eggs: \( 4(1)+9 = 13 \leq 14 \).
• Flour: \( 7(1)+3(9)=7 + 27 = 34 \). But \( 34>32 \), violates flour constraint. Eliminate B.

Step 3: Test Option C (\( x = 2, y = 6 \))

• Eggs: \( 4(2)+6 = 14 \leq 14 \).
• Flour: \( 7(2)+3(6)=14 + 18 = 32 \leq 32 \). Both constraints satisfied.

Step 4: Test Option D (\( x = 5, y = 1 \))

• Eggs: \( 4(5)+1 = 21 \). \( 21>14 \), violates egg constraint. Eliminate D.

Answer:

C. 2 loaves of pumpkin bread and 6 loaves of banana bread