Question

1. a science club has a ratio of chemistry students to physics students of 2:3.

part a: if the club consists only of chemistry and physics students, what is the ratio of chemistry students to total students?
part b: another science club has a ratio of chemistry to physics students of 4:5. if both clubs have 15 physics students, which club has more chemistry students?

Explanation:

Part A

Step1: Define total parts

Total parts = 2 + 3 = 5

Step2: Find chem to total ratio

Ratio = $\frac{\text{Chemistry parts}}{\text{Total parts}} = \frac{2}{5}$

Part B

Step1: Find chem students (Club 1)

Given ratio 2:3, let chem students be $x$. $\frac{x}{15} = \frac{2}{3}$ → $x = \frac{2 \times 15}{3} = 10$

Step2: Find chem students (Club 2)

Given ratio 4:5, let chem students be $y$. $\frac{y}{15} = \frac{4}{5}$ → $y = \frac{4 \times 15}{5} = 12$

Step3: Compare the two values

12 > 10, so Club 2 has more.

Answer:

Part A: $\frac{2}{5}$
Part B: The club with a chemistry to physics student ratio of 4:5 has more chemistry students.