Question

In one week, a music store sold electric guitars for $479 each and acoustic guitars were sold for $339 each. Nine guitars were sold for a total of $3611. How many of each type of guitar were sold this week?

a. 5 electric guitars and 4 acoustic guitars
b. 6 electric guitars and 3 acoustic guitars
c. 4 electric guitars and 5 acoustic guitars
d. 3 electric guitars and 6 acoustic guitars

Answer 1

4 electric guitars and 5 acoustic guitars were sold this week.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's represent the number of electric guitars sold as 'x' and the number of acoustic guitars sold as 'y'. The total number of guitars sold is 9, so we have the equation:

x + y = 9

The total cost of the electric guitars sold is 479x and the total cost of the acoustic guitars sold is 339y. The total cost of all the guitars sold is $3611, so we have the equation:

479x + 339y = 3611

We can solve this system of equations to find the values of x and y. By substituting the value of x from the first equation into the second equation, we get:

479(9 - y) + 339y = 3611

Simplifying the equation gives us:

4311 - 479y + 339y = 3611

Combining like terms gives us:

-140y = -700

Dividing both sides by -140 gives us:

y = 5

Substituting the value of y back into the first equation gives us:

x + 5 = 9

Subtracting 5 from both sides gives us:

x = 4

Therefore, 4 electric guitars and 5 acoustic guitars were sold this week.