26. Christopher orders a 3 topping pizza for $15.35, and a 5 topping pizza for $17.95. Write and solve a system of linear equations to find the price of a plain cheese pizza
(no toppings) and the cost of each topping.

Step-by-step explanation:

Let c represent the price of a cheese pizza (no toppings), and t represent the price of a topping.

  c + 3t = 15.35 . . . . cost of a 3-topping pizza

  c + 5t = 17.95 . . . . cost of a 5-topping pizza

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Subtract the first equation from the second.

  (c +5t) -(c +3t) = (17.95) -(15.35)

  2t = 2.60 . . . simplify [equation 3]

  t = 1.30 . . . . . divide by 2

Then the cost of the cheese pizza is ...

  c = 15.35 -3t = 15.35 -3(1.30) = 11.45

A plain cheese pizza costs $11.45; each topping costs $1.30.

Comment on the working

If you're paying attention to what the problem statement is telling you, you should be able to arrive at "equation 3" without much thought. The 5-topping pizza differs from the 3-topping pizza only in the price of 2 toppings. Once you know the price of a topping, figuring the base price of the pizza is not hard.