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

Answer:

4 electric guitars and and 5 acoustic guitars were sold.

Step-by-step explanation:

Electric guitars:  $x$

Acoustic guitars: $y$

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

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

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

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

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$-140x = -560\\x = \frac{-560}{-140} \\x = 4$

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.