📄 SAT Math: Problem Solving and Data Analysis Worksheet

💡 Solution Steps:

To solve this problem, we first need to find the total number of students surveyed.

<strong>Step 1: Calculate the total number of students.</strong>
Total students = Number of students for Basketball + Soccer + Tennis + Swimming + Other
Total students = \( 150 + 120 + 80 + 50 + 100 = 500 \) students.

<strong>a) What percentage of students chose Soccer as their favorite sport?</strong>
<strong>Step 2: Find the percentage for Soccer.</strong>
Percentage for Soccer = \( \frac{\text{Number of students who chose Soccer}}{\text{Total number of students}} \times 100% \)
Percentage for Soccer = \( \frac{120}{500} \times 100% \)
Percentage for Soccer = \( 0.24 \times 100% = 24% \).

<strong>b) If 20% of the students who chose "Other" were actually undecided and did not choose a specific sport, how many students chose a specific sport?</strong>
<strong>Step 3: Calculate the number of undecided students from the "Other" category.</strong>
Number of students in "Other" category = 100.
20% of these were undecided = \( 0.20 \times 100 = 20 \) students.

<strong>Step 4: Calculate the number of students who chose a specific sport.</strong>
This can be done in two ways:
<strong>Method 1: Subtract undecided students from the total.</strong>
Students who chose a specific sport = Total students - Number of undecided students
Students who chose a specific sport = \( 500 - 20 = 480 \) students.

<strong>Method 2: Sum the specific sports and the remaining 'Other' students.</strong>
Number of 'Other' students who chose a specific (but not listed) sport = \( 100 - 20 = 80 \) students.
Students who chose a specific sport = (Basketball + Soccer + Tennis + Swimming) + (Remaining 'Other' students)
Students who chose a specific sport = \( (150 + 120 + 80 + 50) + 80 \)
Students who chose a specific sport = \( 400 + 80 = 480 \) students.

Therefore, 24% of students chose Soccer, and 480 students chose a specific sport.

💡 Solution Steps:

Let the common multiplier for the ratio be \( x \). This means the weight of flour is \( 5x \), the weight of sugar is \( 3x \), and the weight of butter is \( 2x \).

<strong>Step 1: Determine the value of \( x \) using the given information about sugar.</strong>
We are given that the baker uses 1.5 kg of sugar. So, we can set up the equation:
\( 3x = 1.5 \text{ kg} \)
Divide both sides by 3:
\( x = \frac{1.5}{3} \text{ kg} \)
\( x = 0.5 \text{ kg} \)

<strong>Step 2: Calculate the weight of flour.</strong>
Weight of flour = \( 5x \)
Weight of flour = \( 5 \times 0.5 \text{ kg} \)
Weight of flour = \( 2.5 \text{ kg} \)

<strong>Step 3: Calculate the weight of butter.</strong>
Weight of butter = \( 2x \)
Weight of butter = \( 2 \times 0.5 \text{ kg} \)
Weight of butter = \( 1.0 \text{ kg} \)

<strong>Step 4: Calculate the total weight of the ingredients.</strong>
Total weight = Weight of flour + Weight of sugar + Weight of butter
Total weight = \( 2.5 \text{ kg} + 1.5 \text{ kg} + 1.0 \text{ kg} \)
Total weight = \( 5.0 \text{ kg} \)

Alternatively, using the ratio sum:
Total ratio parts = \( 5 + 3 + 2 = 10 \)
Total weight = \( 10x = 10 \times 0.5 \text{ kg} = 5.0 \text{ kg} \).

Therefore, the baker uses 2.5 kg of flour and 1.0 kg of butter, and the total weight of the ingredients is 5.0 kg.

💡 Solution Steps:

The given equation for the line of best fit is \( y = 5x + 60 \).

a) <strong>Interpret the meaning of the slope.</strong>
<strong>Step 1: Identify the slope.</strong>
In the equation \( y = mx + b \), \( m \) is the slope. Here, the slope is 5.

<strong>Step 2: Interpret the slope in context.</strong>
The slope represents the change in \( y \) for every one-unit increase in \( x \). In this context, for every additional hour a student spends studying (increase in \( x \) by 1), their predicted test score (\( y \)) increases by 5 points. So, the slope of 5 means that, on average, each additional hour of studying is associated with a 5-point increase in the test score.

b) <strong>Predict the test score for a student who studied for 3.5 hours.</strong>
<strong>Step 1: Substitute the value of \( x \) into the equation.</strong>
Given \( x = 3.5 \) hours. Substitute this into \( y = 5x + 60 \):
\( y = 5(3.5) + 60 \)

<strong>Step 2: Calculate the predicted test score.</strong>
\( y = 17.5 + 60 \)
\( y = 77.5 \)

Therefore, a student who studied for 3.5 hours is predicted to achieve a test score of 77.5.

c) <strong>Find the number of hours studied for a student who scored 90 on the test.</strong>
<strong>Step 1: Substitute the value of \( y \) into the equation.</strong>
Given \( y = 90 \). Substitute this into \( y = 5x + 60 \):
\( 90 = 5x + 60 \)

<strong>Step 2: Solve for \( x \).</strong>
Subtract 60 from both sides:
\( 90 - 60 = 5x \)
\( 30 = 5x \)
Divide by 5:
\( x = \frac{30}{5} \)
\( x = 6 \)

Therefore, according to the line of best fit, a student who scored 90 on the test studied for 6 hours.