Math Questions Help!!

45/15*8=24

a):24

24/8*9=27

b):27

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 

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?

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