Question

isaacs favorite drink is a matcha banana smoothie. he wants to make it for a party, but hes not sure how many guests there will be. isaac started making the following chart so he could know how much of each ingredient he would need, depending on the number of guests. fill in the missing numbers in the table below. use the arrow keys or tab to move from one cell to another. to enter a mixed number, press the \+\ key or click the \mixed number\ button below. to view a hint, click in a cell, then press the \h\ key or click the \hint\ button below.

servings	4	2
bananas	4		8
matcha powder (cups)	$\frac{1}{4}$		$\frac{1}{2}$
ice (ounces)	$7\frac{1}{2}$					30
plain yogurt (pints)	$\frac{1}{2}$			$\frac{3}{4}$

Explanation:

( \(\frac{1}{16}\times10\))

• Ice: \(18\frac{3}{4}\) ( \(\frac{75}{4}=18\frac{3}{4}\))
• Plain yogurt: \(1\frac{1}{4}\) ( \(\frac{5}{4}=1\frac{1}{4}\))

Column 6 (Servings = 16):

• Servings: 16 (from ice = 30 ounces: \(30\div\frac{15}{8}=16\))
• Almond milk: 14 ( \(\frac{7}{2}\times4\))
• Bananas: 16 (1 × 16)
• Matcha powder: 1 ( \(\frac{1}{16}\times16\))
• Ice: 30 (given)
• Plain yogurt: 2 ( \(\frac{1}{2}\times4\))

Wait, but let's verify the almond milk for 10 servings: \(\frac{7}{8}\) cups per serving × 10 servings = \(\frac{70}{8}=\frac{35}{4}=8\frac{3}{4}\) cups. Correct.

Now, let's fill the table as per the columns (the original table has columns: 4, 2, [blank], [blank], [blank], [blank] – so the third column is servings = 8, fourth = 6, fifth = 10, sixth = 16? Wait, the original table's third column (the first blank in servings) is where bananas are 8, so servings = 8. Then the fifth column (the fifth cell in servings) has almond milk \(8\frac{3}{4}\), so servings = 10. The sixth column has ice 30, so servings = 16. The fourth column has plain yogurt \(\frac{3}{4}\), so servings = 6.

So to summarize the missing values:

Servings column:

• Third cell: 8
• Fourth cell: 6
• Fifth cell: 10
• Sixth cell: 16

Answer:

( \(\frac{1}{16}\times10\))

• Ice: \(18\frac{3}{4}\) ( \(\frac{75}{4}=18\frac{3}{4}\))
• Plain yogurt: \(1\frac{1}{4}\) ( \(\frac{5}{4}=1\frac{1}{4}\))

Column 6 (Servings = 16):

• Servings: 16 (from ice = 30 ounces: \(30\div\frac{15}{8}=16\))
• Almond milk: 14 ( \(\frac{7}{2}\times4\))
• Bananas: 16 (1 × 16)
• Matcha powder: 1 ( \(\frac{1}{16}\times16\))
• Ice: 30 (given)
• Plain yogurt: 2 ( \(\frac{1}{2}\times4\))

Wait, but let's verify the almond milk for 10 servings: \(\frac{7}{8}\) cups per serving × 10 servings = \(\frac{70}{8}=\frac{35}{4}=8\frac{3}{4}\) cups. Correct.

Now, let's fill the table as per the columns (the original table has columns: 4, 2, [blank], [blank], [blank], [blank] – so the third column is servings = 8, fourth = 6, fifth = 10, sixth = 16? Wait, the original table's third column (the first blank in servings) is where bananas are 8, so servings = 8. Then the fifth column (the fifth cell in servings) has almond milk \(8\frac{3}{4}\), so servings = 10. The sixth column has ice 30, so servings = 16. The fourth column has plain yogurt \(\frac{3}{4}\), so servings = 6.

So to summarize the missing values:

Servings column:

• Third cell: 8
• Fourth cell: 6
• Fifth cell: 10
• Sixth cell: 16