10 waffles and 4 pancakes cost $14. Five waffles and eight pancakes cost $10. How much does a waffle cost? How much does a pancake cost?

9514 1404 393

Step-by-step explanation:

You can model the bills using w and p for the price of a waffle and pancake, respectively.

  10w + 4p = 14

  5w +8p = 10

Subtract half the first equation from the second:

  (5w +8p) -(1/2)(10w +4p) = (10) -(1/2)(14)

  6p = 3 . . . . . . . simplify

  p = 0.50 . . . . . divide by 6

  10w + 4(0.50) = 14 . . . . substitute into the first equation

  10w = 12 . . . . . . . . . . . . subtract 2

  w = 1.20 . . . . . . . . . . . . .divide by 10

A waffle costs $1.20; a pancake costs $0.50.