Forty-five students take piano lessons. The ratio of the numbers of students who take piano lessons to violin lessons is 15:8. The ratio of the numbers of students who take violin lessons to clarinet lessons is 8:9.

a) How many students take violin lessons?

b) How many students take clarinet lessons?

Guest Mar 3, 2017

#2**+5 **

Let V be the number who take violin lessons

a) 45 :/ V = 15 / 8 divide each fraction by 15

3 / V = 1 / 8 cross-multiply

24 = 1V

24 = V

b) Let C be the number who take clarinet lessons

8/9 = V/C

8/9 = 24/C divide each fraction by 8

1/9 = 3/C cross-multiply

1C = 27

C = 27

CPhill
Mar 3, 2017

#3**0 **

**Forty-five students take piano lessons. The ratio of the numbers of students who take piano lessons to violin lessons is 15:8. The ratio of the numbers of students who take violin lessons to clarinet lessons is 8:9.**

**a) How many students take violin lessons?**

\(\begin{array}{|rcll|} \hline && 45\ \text{piano} \cdot \frac{8}{15} \frac{\text{violin}}{\text{piano}} \\ &=& \frac{45\cdot 8}{15}\ \text{violin} \\ &=& 24\ \text{violin} \\ \hline \end{array} \)

**b) How many students take clarinet lessons?**

\(\begin{array}{|rcll|} \hline && 24\ \text{violin} \cdot \frac{9}{8} \frac{\text{clarinet}}{\text{violin}} \\ &=& \frac{24\cdot 9}{8}\ \text{clarinet} \\ &=& 27\ \text{clarinet} \\ \hline \end{array}\)

heureka
Mar 3, 2017