Question

A music store sold a total of 27 used trumpets and clarinets in one month. Trumpets cost $149 and clarinets cost $99. If total sales were $3233, how many clarinets did they sell

Answer 1

The number of clarinets musical store sold was 16. and number of trumpets musical store sold was 11.

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

`x+y=27` ..............(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,
`149x+99y=3233` ...........(2)

Solving for equation (1) and (2),

Multiply equation (1) by 149 , we get

(1) ⇒
`149x+149y=4023` ........(3)

Now, subtract equation (3) from equation (2) , we get

`149x+149y-(149x+99y)=4023-3233`

`\Rightarrow 149x+149y-149x-99y=790`

`\Rightarrow 149y-99y=790`

`\Rightarrow 50y =790`

`\Rightarrow y =(790)/(50)=15.8`

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

`x+y=27 \Rightarrow x+16=27 \Rightarrow x=27-16=11`

Thus, number of trumpets musical store sold was 11.