Question

sofia’s favorite drink is a strawberry rhubarb milkshake. she wants to make it for a party, but she’s not sure how many guests there will be. sofia started making the following chart so she could know how much of each ingredient she would need, depending on the number of guests. fill in the missing numbers in the table below. 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	10	5	20	\boxed{}	1	16
sugar (cups)	$\frac{3}{4}$	\boxed{}	$1\frac{1}{2}$	$1\frac{1}{8}$	$\frac{3}{40}$	$1\frac{1}{5}$
orange zest (teaspoons)	$1\frac{1}{4}$	$\frac{5}{8}$	$2\frac{1}{2}$	$1\frac{7}{8}$	\boxed{}	2
milk (cups)	$2\frac{1}{2}$	$1\frac{1}{4}$	5	$3\frac{3}{4}$	$\frac{1}{4}$	4
strawberry ice cream (pints)	$6\frac{1}{4}$	$3\frac{1}{8}$	\boxed{}	$9\frac{3}{8}$	$\frac{5}{8}$	10

Explanation:

To solve for the missing values, we first determine the "per serving" amount for each ingredient using the given data (e.g., 10 servings) and then use that to find other values.

1. Servings (Unknown Value)

We use the rhubarb column. For 10 servings, rhubarb is \( 7\frac{1}{2} \) cups. The per - serving rhubarb is \( 7\frac{1}{2}\div10=\frac{15}{2}\div10=\frac{15}{2}\times\frac{1}{10}=\frac{3}{4} \) cup per serving (matches the 1 - serving value).
Let the unknown servings be \( x \). We know that for \( x \) servings, rhubarb is \( 11\frac{1}{4}=\frac{45}{4} \) cups. Since per serving is \( \frac{3}{4} \) cup, we solve \( \frac{3}{4}x=\frac{45}{4} \).
Multiply both sides by \( \frac{4}{3} \): \( x = \frac{45}{4}\times\frac{4}{3}=15 \).

2. Rhubarb for 16 Servings

Per serving rhubarb is \( \frac{3}{4} \) cup. For 16 servings, rhubarb is \( \frac{3}{4}\times16 = 12 \) cups.

3. Sugar for 5 Servings

For 10 servings, sugar is \( \frac{3}{4} \) cup. Per serving sugar is \( \frac{3}{4}\div10=\frac{3}{40} \) cup (matches the 1 - serving value). For 5 servings, sugar is \( \frac{3}{40}\times5=\frac{3}{8} \) cup.

4. Orange Zest for 1 Serving

For 10 servings, orange zest is \( 1\frac{1}{4}=\frac{5}{4} \) teaspoons. Per serving orange zest is \( \frac{5}{4}\div10=\frac{5}{4}\times\frac{1}{10}=\frac{1}{8} \) teaspoon.

5. Strawberry Ice Cream for 20 Servings

For 10 servings, strawberry ice cream is \( 6\frac{1}{4}=\frac{25}{4} \) pints. Per serving is \( \frac{25}{4}\div10=\frac{25}{4}\times\frac{1}{10}=\frac{5}{8} \) pint (matches the 1 - serving value). For 20 servings, it is \( \frac{5}{8}\times20=\frac{100}{8}=12\frac{1}{2} \) pints.

Final Table (Key Missing Values):

Servings	10	5	20	15	1	16
sugar (cups)	\( \frac{3}{4} \)	\( \frac{3}{8} \)	\( 1\frac{1}{2} \)	\( 1\frac{1}{8} \)	\( \frac{3}{40} \)	\( 1\frac{1}{5} \)
orange zest (teaspoons)	\( 1\frac{1}{4} \)	\( \frac{5}{8} \)	\( 2\frac{1}{2} \)	\( 1\frac{7}{8} \)	\( \frac{1}{8} \)	2
milk (cups)	\( 2\frac{1}{2} \)	\( 1\frac{1}{4} \)	5	\( 3\frac{3}{4} \)	\( \frac{1}{4} \)	4
strawberry ice cream (pints)	\( 6\frac{1}{4} \)	\( 3\frac{1}{8} \)	\( 12\frac{1}{2} \)	\( 9\frac{3}{8} \)	\( \frac{5}{8} \)	10

Specific Answers (As per Table Cells):

• Servings (unknown): \( \boldsymbol{15} \)
• Rhubarb (16 servings): \( \boldsymbol{12} \)
• Sugar (5 servings): \( \boldsymbol{\frac{3}{8}} \)
• Orange Zest (1 serving): \( \boldsymbol{\frac{1}{8}} \)
• Strawberry Ice Cream (20 servings): \( \boldsymbol{12\frac{1}{2}} \)

Answer:

To solve for the missing values, we first determine the "per serving" amount for each ingredient using the given data (e.g., 10 servings) and then use that to find other values.

1. Servings (Unknown Value)

We use the rhubarb column. For 10 servings, rhubarb is \( 7\frac{1}{2} \) cups. The per - serving rhubarb is \( 7\frac{1}{2}\div10=\frac{15}{2}\div10=\frac{15}{2}\times\frac{1}{10}=\frac{3}{4} \) cup per serving (matches the 1 - serving value).
Let the unknown servings be \( x \). We know that for \( x \) servings, rhubarb is \( 11\frac{1}{4}=\frac{45}{4} \) cups. Since per serving is \( \frac{3}{4} \) cup, we solve \( \frac{3}{4}x=\frac{45}{4} \).
Multiply both sides by \( \frac{4}{3} \): \( x = \frac{45}{4}\times\frac{4}{3}=15 \).

2. Rhubarb for 16 Servings

Per serving rhubarb is \( \frac{3}{4} \) cup. For 16 servings, rhubarb is \( \frac{3}{4}\times16 = 12 \) cups.

3. Sugar for 5 Servings

For 10 servings, sugar is \( \frac{3}{4} \) cup. Per serving sugar is \( \frac{3}{4}\div10=\frac{3}{40} \) cup (matches the 1 - serving value). For 5 servings, sugar is \( \frac{3}{40}\times5=\frac{3}{8} \) cup.

4. Orange Zest for 1 Serving

For 10 servings, orange zest is \( 1\frac{1}{4}=\frac{5}{4} \) teaspoons. Per serving orange zest is \( \frac{5}{4}\div10=\frac{5}{4}\times\frac{1}{10}=\frac{1}{8} \) teaspoon.

5. Strawberry Ice Cream for 20 Servings

For 10 servings, strawberry ice cream is \( 6\frac{1}{4}=\frac{25}{4} \) pints. Per serving is \( \frac{25}{4}\div10=\frac{25}{4}\times\frac{1}{10}=\frac{5}{8} \) pint (matches the 1 - serving value). For 20 servings, it is \( \frac{5}{8}\times20=\frac{100}{8}=12\frac{1}{2} \) pints.

Final Table (Key Missing Values):

Servings	10	5	20	15	1	16
sugar (cups)	\( \frac{3}{4} \)	\( \frac{3}{8} \)	\( 1\frac{1}{2} \)	\( 1\frac{1}{8} \)	\( \frac{3}{40} \)	\( 1\frac{1}{5} \)
orange zest (teaspoons)	\( 1\frac{1}{4} \)	\( \frac{5}{8} \)	\( 2\frac{1}{2} \)	\( 1\frac{7}{8} \)	\( \frac{1}{8} \)	2
milk (cups)	\( 2\frac{1}{2} \)	\( 1\frac{1}{4} \)	5	\( 3\frac{3}{4} \)	\( \frac{1}{4} \)	4
strawberry ice cream (pints)	\( 6\frac{1}{4} \)	\( 3\frac{1}{8} \)	\( 12\frac{1}{2} \)	\( 9\frac{3}{8} \)	\( \frac{5}{8} \)	10

Specific Answers (As per Table Cells):

• Servings (unknown): \( \boldsymbol{15} \)
• Rhubarb (16 servings): \( \boldsymbol{12} \)
• Sugar (5 servings): \( \boldsymbol{\frac{3}{8}} \)
• Orange Zest (1 serving): \( \boldsymbol{\frac{1}{8}} \)
• Strawberry Ice Cream (20 servings): \( \boldsymbol{12\frac{1}{2}} \)