Answer-
The store is charging $3.39 for a carton of eggs.
Solution-
Let us assume that,
Price of each cartons of egg = x
Price of each loaves of bread = y
Kate bought 3 cartons of eggs and 5 loaves of bread and spent $30.07,
[tex]\Rightarrow 3x+5y=30.07[/tex] --------------1
Melissa bought 2 cartons of eggs and 2 loaves of bread and spent $14.74,
[tex]\Rightarrow 2x+2y=14.74[/tex]
[tex]\Rightarrow x+y=\dfrac{14.74}{2}[/tex]
[tex]\Rightarrow x+y=7.37[/tex]
[tex]\Rightarrow y=7.37-x[/tex] ------------------2
Putting equation 2 in equation 1,
[tex]\Rightarrow 3x+5(7.37-x)=30.07[/tex]
[tex]\Rightarrow 3x+36.85-5x=30.07[/tex]
[tex]\Rightarrow 3x-5x=30.07-36.85[/tex]
[tex]\Rightarrow -2x=-6.78[/tex]
[tex]\Rightarrow 2x=6.78[/tex]
[tex]\Rightarrow x=\dfrac{6.78}{2}[/tex]
[tex]\Rightarrow x=3.39[/tex]
Therefore, the price of a carton of egg is $3.39
