SaiBook.us SAT-3

Lesson Example Discussion Quiz: Class Homework

Example

Title: Statistics

Grade: Best-SAT3 Lesson: S8-P1

Explanation: The best way to understand SAT-3 is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

You and your friend are at the movie theater. Popcorn costs $x per bag and drinks cost $y each. If you buy 2 bags of popcorn and 1 drink, how much will it cost in total? This can be represented by the equation 2x + 1y = total cost. You can then plug in different prices for x and y to find the total cost for different scenarios.

Step 1a

You and your friend are at the movie theater. Popcorn costs x dollars per bag and drinks cost y dollars each. You decide to buy 2 bags of popcorn and 1 drink. The total cost can be represented by the equation: 2x + y = total cost
Variables:
→ 𝑥: Cost of one bag of popcorn
→ 𝑦: Cost of one drink

Explanation: Here, we write the formula and variables.

Step 1b

Data:
Let’s consider different scenarios with varying costs for popcorn and drinks.

Scenario 1:
Cost of popcorn (𝑥): $5 per bag
Cost of drink (𝑦): $3 each
Total cost: 2(5) + 3 = 10 + 3 = 13 dollars

Scenario 2:
Cost of popcorn (𝑥): $4 per bag
Cost of drink (𝑦): $2 each
Total cost: 2(4) + 2 = 8 + 3 = 11 dollars

Scenario 3:
Cost of popcorn (𝑥): $6 per bag
Cost of drink (𝑦): $4 each
Total cost: 2(6) + 4 = 12 + 4 = 16 dollars

Scenario 4:
Cost of popcorn (𝑥): $3 per bag
Cost of drink (𝑦): $5 each
Total cost: 2(3) + 5 = 6 + 5 = 11 dollars

Explanation: Here, we write different scenarios.

Step 1c

Explanation:
→ Variables: The two variables in this problem are the cost of a bag of popcorn (x) and the cost of a drink (y).

→ Equation: The equation 2x + y = total cost represents the total cost for 2 bags of popcorn and 1 drink.

Analysis:
By plugging different values for x and y into the equation, you can calculate the total cost for various pricing scenarios. This helps in understanding how changes in the prices of popcorn and drinks affect the total expenditure.

Explanation: Here, we write an explanation and analysis.

Step 1d

$1d$

Explanation: Here, we can represent the data in a table format. Therefore, the total cost will depend on the specific prices of popcorn (𝑥) and drinks (𝑦) that you use in the equation.

A market researcher randomly selected 200 people who had expressed that they liked a particular book. These individuals were shown a movie adaptation of the book and were then asked if they liked or disliked the movie. Of those surveyed, 95% reported that they disliked the movie. Calculate the number of people who disliked the movie.

Step 2a

Determine the total number of people surveyed: 200
Identify the percentage of people who disliked the movie: 95%

Calculate the number of people who disliked the movie:
Since 95% of the 200 people disliked the movie, convert 95% to a decimal: 95% = 0.95
Multiply the total number of people by the percentage:
\$200 \times 0.95 = 190\$

Explanation: Therefore, the number of people who disliked the movie was 190.