Question

In one week, a music store sold 9 guitars for a total of $3611. Electric guitars sold for $479

each and acoustic guitars sold for $339 each. Write and solve a system of equations to
determine how many of each type of guitar was sold.

Answer 1

4 electric guitars and and 5 acoustic guitars were sold.

Explanation:

Electric guitars:
`x`

Acoustic guitars:
`y`

`y + x = 9\\y(339) + x(479) = 3611\\`

--------------------------------

`y + x = 9\\339y + 479x = 3611`

--------------------------------

`(y + x = 9)339\\(339y + 479x = 3611)1`

--------------------------------

`339y + 339x = 3051\\339y + 479x = 3611`

--------------------------------

`-140x = -560\\x = (-560)/(-140) \\x = 4`

Choose any of the two equations in the first step and substitute 4 for
`x`.

`y + 4 = 9\\y = 9 - 4\\y = 5`

Therefore, there are 4 electric guitars and and 5 acoustic guitars were sold.

Note: In the elimination method of simultaneous equations, (+) + (+) = (-); (+) + (-) = (+) and (-) + (+) = (+) the signs addition or subtraction.