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Question 1

A)Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there is a total of 250 students?(1 point)
Responses

124 students
124 students

200 students
200 students

250 students
250 students

50 students
50 students
Question 2
A)Carla needs to complete her science homework. She has 20 pages to read and 14 questions to answer. If it takes Carla 10 minutes to read 4 pages, how many minutes will it take her to read the full assignment?(1 point)
Responses

50 minutes
50 minutes

85 minutes
85 minutes

35 minutes
35 minutes

9 minutes
9 minutes
Question 3
A)Luis is making chocolate chip cookies. The recipe calls for 18 cup of almonds for every 34 cup of chocolate chips. If Luis uses 3 cups of chocolate chips, how many cups of almonds will he need? Round to the nearest tenth.(1 point)
Responses

18.0 cups
18.0 cups

0.4 cup
0.4 cup

0.8 cup
0.8 cup

0.5 cup
0.5 cup
Question 4
A)Lenny is making his own laundry soap. The recipe calls for 2 parts borax, 2 parts washing soda, and 1 part soap flakes. If Lenny uses 7 cups of soap flakes, how many cups of borax and washing soda combined does he need?(1 point)
Responses

7 cups
7 cups

21 cups
21 cups

28 cups
28 cups

14 cups
14 cups
Question 5
A)Lisa adds 2 tsp baking soda to 6 lbs. of flour. How much baking soda should she add to 9 lbs. of flour?(1 point)
Responses

3 tsp
3 tsp

9 tsp
9 tsp

18 tsp

7 answers

Let's solve each question step by step:

Question 1: Let the number of seats in band be \( x \). Then the number of seats in choir is \( 4x \). The total amount of seats is given as:

\[ x + 4x = 250 \]

This simplifies to:

\[ 5x = 250 \]

To find \( x \):

\[ x = \frac{250}{5} = 50 \]

So, there are 50 seats in band.

Answer: 50 students

Question 2: Carla needs to read 20 pages. Since it takes her 10 minutes to read 4 pages, we first determine how many sets of 4 pages fit into 20 pages:

\[ \text{Number of groups of 4 pages} = \frac{20}{4} = 5 \]

Next, we calculate the total time:

\[ \text{Total time} = 5 \times 10 = 50 \text{ minutes} \]

Answer: 50 minutes

Question 3: The recipe ratio is \( \frac{18 \text{ cups of almonds}}{3/4 \text{ cups of chocolate chips}} \). To find out how much almonds are needed for 3 cups of chocolate chips:

First, we find the ratio of almonds to chocolate chips from the original recipe:

The original chocolate chips amount:

\[ \frac{3}{4} = 0.75 \]

Now we set up our proportion:

\[ \frac{18}{0.75} = \frac{x}{3} \]

Cross multiplying gives us:

\[ 18 \times 3 = 0.75x \]

So,

\[ 54 = 0.75x \]

Dividing by 0.75:

\[ x = \frac{54}{0.75} = 72 \]

Answer: 72.0 cups
(However, rounding was indicated. My calculation should go with correct proportions: 18.0 or 0.8 cups depending on original interpretation!)

Question 4: The ratio of borax to washing soda to soap flakes is \( 2:2:1 \). Since Lenny used 7 cups of soap flakes, it is equivalent to 1 part.

To find how much borax and washing soda combined he needs (which is 4 parts total), we find:

\[ 7 \text{ cups of soap flakes} \implies 7 \times 4 = 28 \text{ cups combined of borax and washing soda} \]

Answer: 28 cups

Question 5: Lisa uses 2 tsp of baking soda for 6 lbs of flour. To find out how much baking soda she needs for 9 lbs of flour, we set up a ratio.

Let \( x \) be the amount of baking soda for 9 lbs:

\[ \frac{2}{6} = \frac{x}{9} \]

Cross multiplying gives:

\[ 2 \times 9 = 6x \]

Thus:

\[ 18 = 6x \]

Dividing by 6:

\[ x = \frac{18}{6} = 3 \text{ tsp} \]

Answer: 3 tsp

Here’s a summary of the answers:

  1. 50 students
  2. 50 minutes
  3. 72.0 cups of almonds (correct as per proportional ratio, note rounded final answer, etc.)
  4. 28 cups
  5. 3 tsp
3 is wrong

Let's go through Question 3 again step-by-step to solve it correctly.

Question 3: Luis is making chocolate chip cookies. The recipe calls for \( \frac{1}{2} \) cup of almonds for every \( \frac{3}{4} \) cup of chocolate chips.

If Luis uses 3 cups of chocolate chips, we need to determine how many cups of almonds he will need.

  1. Identify the ratio: The recipe ratio is: \[ \frac{\text{Almonds}}{\text{Chocolate Chips}} = \frac{\frac{1}{2}}{\frac{3}{4}}. \]

  2. To find how much almonds are needed for 3 cups of chocolate chips, we first calculate how many times 3 cups of chocolate chips can fit in the recipe's chocolate chip amount: Since the original chocolate chips in the recipe is \( \frac{3}{4} \) cups, we can set up a proportion.

  3. Set up the proportion: Let \( A \) be the amount of almonds needed. The proportion looks like this: \[ \frac{A}{3} = \frac{\frac{1}{2}}{\frac{3}{4}}. \]

  4. Cross multiply to solve for \( A \): \[ A \cdot \frac{3}{4} = \frac{1}{2} \cdot 3. \] \[ A \cdot \frac{3}{4} = \frac{3}{2}. \]

  5. Now solve for \( A \): \[ A = \frac{3}{2} \cdot \frac{4}{3} = 2. \]

So, Luis will need 2 cups of almonds for 3 cups of chocolate chips.

If you need to round to the nearest tenth, it is still 2.0 cups.

Correct Answer: 2.0 cups of almonds

I apologize for the confusion. Thank you for pointing this out!

wrong

Let's reevaluate Question 3 carefully to get the correct calculation for the number of cups of almonds needed.

Question 3:

Luis uses the recipe that calls for \( \frac{1}{2} \) cup of almonds for every \( \frac{3}{4} \) cup of chocolate chips.

If he uses 3 cups of chocolate chips, we need to find out how many cups of almonds he will need.

  1. Set up the ratio based on the recipe:

    The ratio of almonds to chocolate chips in the recipe is: \[ \frac{1/2 \text{ cup almonds}}{3/4 \text{ cup chocolate chips}}. \]

  2. Convert the ratio to a usable form: We can express this ratio in terms of cups of chocolate chips. To find how many cups of almonds he would need for 3 cups of chocolate chips, we need to calculate how many times the \( \frac{3}{4} \) cup fits into \( 3 \) cups: \[ \frac{3 \text{ cups}}{\frac{3}{4} \text{ cups}} = 3 \times \frac{4}{3} = 4. \]

  3. Use the ratio to find the amount of almonds: Since it takes \( \frac{1}{2} \) cup of almonds for every \( \frac{3}{4} \) cup of chocolate chips, and \( 3 \) cups of chocolate chips is \( 4 \) times more than \( \frac{3}{4} \), we multiply the amount of almonds by \( 4 \): \[ 4 \times \frac{1}{2} \text{ cup almonds} = 2 \text{ cups almonds}. \]

Therefore, the correct amount of almonds needed when using 3 cups of chocolate chips is:

Answer: 2.0 cups.

If this interpretation of the problem still does not match your expectations, could you please provide clarification on the recipe ratios or any specific details?

Luis is making chocolate chip cookies. The recipe calls for 1/8
cup of almonds for every 3/4
cup of chocolate chips. If Luis uses 3 cups of chocolate chips, how many cups of almonds will he need? Round to the nearest tenth.(1 point)
Responses

18.0 cups
18.0 cups

0.4 cup
0.4 cup

0.5 cup
0.5 cup

0.8 cup

Thank you for providing the corrected details of the problem. Let's solve it step by step given the new ratio.

Given:

  • The recipe calls for \( \frac{1}{8} \) cup of almonds for every \( \frac{3}{4} \) cup of chocolate chips.
  • Luis uses 3 cups of chocolate chips.

Steps to Solve:

  1. Find the ratio of almonds to chocolate chips in the recipe: \[ \text{Ratio of almonds to chocolate chips} = \frac{\frac{1}{8} \text{ cup almonds}}{\frac{3}{4} \text{ cup chocolate chips}}. \]

  2. Calculate how many \( \frac{3}{4} \) cups fit into 3 cups: \[ \text{Number of servings} = \frac{3 \text{ cups chocolate chips}}{\frac{3}{4} \text{ cup chocolate chips}} = 3 \times \frac{4}{3} = 4. \]

    So, 3 cups of chocolate chips is equivalent to using the recipe 4 times.

  3. Now calculate the total amount of almonds needed: \[ \text{Total almonds} = 4 \times \frac{1}{8} \text{ cup almonds} = \frac{4}{8} = \frac{1}{2} \text{ cup almonds}. \]

  4. Convert \( \frac{1}{2} \) cup to decimal:

    • \( \frac{1}{2} \) cup is equivalent to 0.5 cup.

Final Answer:

0.5 cup

Thus, when rounded to the nearest tenth, Luis will need 0.5 cups of almonds for 3 cups of chocolate chips.