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?
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
