Question

Kate and Melisa both went to the same store to buy eggs and bread for their families. Kate bought 3 cartons of eggs and 5 loaves of bread; she spent $30.07. Melissa purchased 2 cartons of eggs and 2 loaves of bread; she spent $14.74. What is the store charging for a carton of eggs?

Answer 1

Write an equation system based on the problem
For an instance, e stands for the price of a carton of eggs, and b stands for the price of a loaf of bread

"Kate bought 3 cartons of eggs and 5 loaves of bread for $30.07" could be written as 3e + 5b = 30.07 (first equation)
"Melissa bought 2 cartons of eggs and 2 loaves of bread for $14.74" could be written as 2e + 2b = 14.74 (second equation)

Solve the equation system using elimination method
Eliminate b to find e. To eliminate b, we should equalize the coefficient of b.
3e + 5b = 30.07 (multiplied by 2)
2e + 2b = 14.74 (multiplied by 5)
-------------------------------------------
  6e + 10b = 60.14
10e + 10b = 73.70
------------------------- - (substract)
-4e            = -13.56
   e            = -13.56/-4
   e            = 3.39

The price for a carton of eggs is $3.39