Respuesta :
Answer:
The number of clarinets musical store sold was 16. and number of trumpets musical store sold was 11.
Step-by-step explanation:
Let the musical store sells 'x' number of trumpets and 'y' number of clarinets.
According to question,
Total number of trumpets and clarinets sold is 27 that is
[tex]x+y=27[/tex] ..............(1)
Also given Trumpets cost $149 and clarinets cost $99.
then the shop sold x trumpets for $149x and sold y clarinets for $99y and total sales were $3233.
thus, [tex]149x+99y=3233[/tex] ...........(2)
Solving for equation (1) and (2),
Multiply equation (1) by 149 , we get
(1) ⇒ [tex]149x+149y=4023[/tex] ........(3)
Now, subtract equation (3) from equation (2) , we get
[tex]149x+149y-(149x+99y)=4023-3233[/tex]
[tex]\Rightarrow 149x+149y-149x-99y=790[/tex]
[tex]\Rightarrow 149y-99y=790[/tex]
[tex]\Rightarrow 50y =790[/tex]
[tex]\Rightarrow y =\frac{790}{50}=15.8[/tex]
Thus, number of clarinets musical store sold was 15.8 but since clarinets are to be in whole number rounding off to the nearest integer 16.
and put y = 16 in (1) , we get
[tex]x+y=27 \Rightarrow x+16=27 \Rightarrow x=27-16=11[/tex]
Thus, number of trumpets musical store sold was 11.
