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Math Questions Help!!

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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

#1
+321
+5

45/15*8=24

a):24

24/8*9=27

b):27

Davis  Mar 3, 2017
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#1
+321
+5

45/15*8=24

a):24

24/8*9=27

b):27

Davis  Mar 3, 2017
#2
+77034
+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
+18624
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

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