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A guitar shop is offering two deals on their guitars. Each guitar is $50 less than its initial sale price. In addition, customers receive a further discount of $3 off each $5 of the sale price. Write a function that represents the final price of a guitar f(x) with an initial price of x. If a guitars initial price was $200, what would it be with the discount?

Using the discount parameters given, the final sale price function of the guitar would be f(x) = x - 0.6x - 30 and the discount on initial price of $200 would be $90

Let initial price = x

First discount :

$50 off :

f(x) = x - 50

Second discount :

$3 off each $5 of sale price

3/5 of sale price = 0.6 × (x - 50)

Final discount :

0.6( x - 50) = 0.6x - 30

The Final sale price :

f(x) = x - 0.6x - 30

Given an initial price, x = 200

Discount on price :

Final discount = 0.6x - 30

Discount on price of x = 200 :

0.6(200) - 30

120 - 30 = $90

Therefore, the discount on the price is $90

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