The function c(x) = 17.5x - 10 represents the cost (in dollars) of buying x tickets to the orchestra with a $10 coupon. a. how much cost to buy 10 tickets? b. how many tickets can you buy with $130?

The cost function is a linear function

The cost of 10 tickets is $165You can buy 8 tickets with $130

The function is given as:

(a) The cost of 10 tickets

This means that: x= 10

So, we have:

Hence, the cost of 10 tickets is $165

(b) The number of tickets that costs $130

This means that C(x) = 130

So, we have:

Add 10 to both sides

Divide both sides by 17.5

Rewrite as:

Hence, you can buy 8 tickets with $130

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a. How much cost to buy 10 tickets?
 For this case what you must do is replace the value of x = 10 in the given equation.
 We have then:
 C (x) = 17.5x - 10
 C (10) = 17.5 * (10) - 10
 C (10) = 165
 
 to buy 10 tickets cost:
 $ 165

 b. How many tickets can you buy with $ 130? 
 For this case we must make the substitution: C (x) = 130
 We have then:
 C (x) = 17.5x - 10
 130 = 17.5x - 10
 Clearing x we have:
 17.5x = 130 + 10
 17.5x = 140
 x = (140) / (17.5)
 x = 8
 
 You can buy 8 tickets with $ 130

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