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?
+128474 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
+26367 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?
\(\begin{array}{|rcll|} \hline && 24\ \text{violin} \cdot \frac{9}{8} \frac{\text{clarinet}}{\text{violin}} \\ &=& \frac{24\cdot 9}{8}\ \text{clarinet} \\ &=& 27\ \text{clarinet} \\ \hline \end{array}\)
