On Fridays, students in Mr. Lee's gym class can either play basketball or badminton. Last week, 15 students played basketball. The ratio of students who played basketball to badminton was 3:2.

Question

How many total students were in Mr. Lee's gym class last Friday?

Answer 1

Let the number of students who played badminton be denoted as \( b \). According to the information given, the ratio of students who played basketball to badminton is 3:2. This can be represented mathematically as:

\[ \frac{\text{students playing basketball}}{\text{students playing badminton}} = \frac{3}{2} \]

From the problem, we know that 15 students played basketball:

\[ \frac{15}{b} = \frac{3}{2} \]

To find \( b \), we can cross-multiply:

\[ 15 \cdot 2 = 3 \cdot b \]

\[ 30 = 3b \]

Now, dividing both sides by 3 gives us:

\[ b = \frac{30}{3} = 10 \]

Thus, the number of students who played badminton is 10.

To find the total number of students in Mr. Lee's gym class, we add the number of students who played basketball with those who played badminton:

\[ \text{Total students} = \text{students playing basketball} + \text{students playing badminton} = 15 + 10 = 25 \]

Therefore, the total number of students in Mr. Lee's gym class last Friday was \( \boxed{25} \).

Answer 2

Jon is making fresh-squeezed orange juice. There is a proportional relationship between x, the number of oranges Jon squeezes, and y, the amount of juice he makes in ounces.
After squeezing 4 oranges, Jon has 8 ounces of juice. Write the equation for the relationship between x and y.

Answer 3

To establish the relationship between the number of oranges squeezed (x) and the amount of juice made in ounces (y), we start by recognizing that this is a proportional relationship. This can be expressed with the equation:

\[ y = kx \]

where \( k \) is the constant of proportionality.

From the information provided, when \( x = 4 \) oranges, Jon produces \( y = 8 \) ounces of juice. We can use this information to solve for \( k \):

\[ 8 = k \cdot 4 \]

To find \( k \), divide both sides by 4:

\[ k = \frac{8}{4} = 2 \]

Now that we have found \( k \), we can write the equation that describes the relationship between \( x \) and \( y \):

\[ y = 2x \]

This equation indicates that for every orange Jon squeezes, he produces 2 ounces of juice. Thus, the equation for the relationship between the number of oranges and the amount of juice is:

\[ \boxed{y = 2x} \]